Algebra for algebraic topology
My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:
What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).
I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.
at.algebraic-topology ac.commutative-algebra homological-algebra
asked 8 hours ago
Piotr Hajlasz
6,02142253
|
show 1 more comment
My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:
What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).
I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.
at.algebraic-topology ac.commutative-algebra homological-algebra
asked 8 hours ago
Piotr Hajlasz
6,02142253
1
That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
8 hours ago
@NeilStrickland I added more details to my question.
– Piotr Hajlasz
8 hours ago
Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
8 hours ago
3
@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
7 hours ago
2
amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
2 hours ago
|
show 1 more comment
My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:
What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).
I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.
at.algebraic-topology ac.commutative-algebra homological-algebra
asked 8 hours ago
Piotr Hajlasz
6,02142253
My research is in analysis, but it moved to the area that requires algebraic topology. I have some working knowledge in that area, but I always feel that I am on a shaky ground and I need to go back and study algebraic topology again. However, that would also require refreshing my knowledge in algebra. My question is:
What is a good reference from which I could learn algebra necessary
for studying algebraic topology at the level of Hatcher's Algebraic Topology plus Eilenberg-Steenrod's axioms (not included in Hatcher's book) plus spectral sequences (in unpublished notes of Hatcher).
I would love to find an elementary reference that would cover all necessary algebraic tools (including homological algebra) on no more than 100$pmvarepsilon$ pages.
at.algebraic-topology ac.commutative-algebra homological-algebra
at.algebraic-topology ac.commutative-algebra homological-algebra
asked 8 hours ago
Piotr Hajlasz
6,02142253
asked 8 hours ago
Piotr Hajlasz
6,02142253
edited 8 hours ago
asked 8 hours ago
Piotr Hajlasz
6,02142253
asked 8 hours ago
Piotr Hajlasz
6,02142253
asked 8 hours ago
Piotr Hajlasz
6,02142253
6,02142253
1
That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
8 hours ago
@NeilStrickland I added more details to my question.
– Piotr Hajlasz
8 hours ago
Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
8 hours ago
3
@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
7 hours ago
2
amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
2 hours ago
|
show 1 more comment
1
That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
8 hours ago
@NeilStrickland I added more details to my question.
– Piotr Hajlasz
8 hours ago
Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
8 hours ago
3
@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
7 hours ago
2
amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
2 hours ago
1
1
That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
8 hours ago
That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
8 hours ago
@NeilStrickland I added more details to my question.
– Piotr Hajlasz
8 hours ago
@NeilStrickland I added more details to my question.
– Piotr Hajlasz
8 hours ago
Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
8 hours ago
Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
8 hours ago
3
3
@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
7 hours ago
@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
7 hours ago
2
2
amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
2 hours ago
amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
2 hours ago
|
show 1 more comment
1 Answer
1
active
oldest
votes
If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.
answered 7 hours ago
Vincenzo Zaccaro
346312
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
3
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
add a comment |
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1 Answer
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1 Answer
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active
oldest
votes
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active
oldest
votes
If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.
answered 7 hours ago
Vincenzo Zaccaro
346312
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
3
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
add a comment |
If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.
answered 7 hours ago
Vincenzo Zaccaro
346312
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
3
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
add a comment |
If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.
answered 7 hours ago
Vincenzo Zaccaro
346312
If you need a concise but very clear book which covers a lot of Algebraic Topology and just the necessary algebra (spectral sequences as well) I think that Differential Forms in Algebraic Topology- Bott & Tu is the book you are looking for.
answered 7 hours ago
Vincenzo Zaccaro
346312
answered 7 hours ago
Vincenzo Zaccaro
346312
answered 7 hours ago
Vincenzo Zaccaro
346312
answered 7 hours ago
Vincenzo Zaccaro
346312
346312
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
3
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
add a comment |
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
3
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
I know this book, but it does not really provides a good introduction to algebra. Moreover, the deRham approach to topology gives only real coefficients and neglects the torsion part.
– Piotr Hajlasz
7 hours ago
3
3
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
Ah! Probably I found the right textbook! Try to take a look at Topology and geometry-Bredon :) It covers the necessary algebra along the way and begins with the basic topics of Algebraic Topology.
– Vincenzo Zaccaro
7 hours ago
add a comment |
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That depends very much on what parts of algebraic topology you want to use and for what purpose. Further details would be helpful.
– Neil Strickland
8 hours ago
@NeilStrickland I added more details to my question.
– Piotr Hajlasz
8 hours ago
Serge Lang's Algebra covers what you need, but it's more than 100 pages. Dummit and Foot is a nice undergraduate algebra book that covers essentially all you need, although it does not really develop homological algebra -- but you don't really need to know any homological algebra to study from Hatcher's book. Dummit and Foot is also over 100 pages. I imagine there is something that satisfies all your criteria. The undergraduate books all are a little longwinded compared to what you are looking for.
– Ryan Budney
8 hours ago
3
@RyanBudney Dummit and Foote: 932 pages, Lang: 914 pages. That is precisely what I would like to avoid. I actually do not like the book by Dummit and Foote: a lot of unnecessary words, like in most of the undergraduate texts.
– Piotr Hajlasz
7 hours ago
2
amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/… is again long, but covers much more ground than Dummit & Foote (and you can safely skip the irrelevant to you chapters, it's much nicer structured than D and F IMHO)
– Dima Pasechnik
2 hours ago