- #1

- 2,255

- 1

I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.

- Thread starter pivoxa15
- Start date

- #1

- 2,255

- 1

I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.

- #2

- 453

- 0

Rotman is good. I think Hatcher is really hard to follow, though others like him.

- #3

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,778

- 11

- #4

Chris Hillman

Science Advisor

- 2,345

- 8

I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.

- #5

- 2,255

- 1

I've got Greenberg and Harper beside me. It looks formidable/impossible due to as you say not many words.

I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.

I'm looking for a dummies book, if there is one.

Aren't you a physcist? If so which area in physics? You seem to be keen with maths as well?

- #6

JasonRox

Homework Helper

Gold Member

- 2,314

- 3

I would try Munkres.

- #7

- 2,255

- 1

His 'Topology'?

- #8

JasonRox

Homework Helper

Gold Member

- 2,314

- 3

Of course.

- #9

- 2

- 0

i think you are looking for "Algebraic Topology: An Introduction" by William S. Massey

- #10

xristy

Gold Member

- 116

- 2

- #11

- 83

- 0

- #12

- 2

- 0

- #13

MathematicalPhysicist

Gold Member

- 4,297

- 205

It's not!Algebraic topology for dummies?

- #14

MathematicalPhysicist

Gold Member

- 4,297

- 205

After his take, one procceeds to Edwin Spanier (Though I haven't yet, and probably will not have time either way to finish Munkers and even starting Spanier).

- #15

mathwonk

Science Advisor

Homework Helper

- 10,994

- 1,186

i have not read his book recommended above including an introduction to singular homology (basic course...) but in grad school his little book on the fundamental group was the only one i could understand, and later his book which serves as the first 5 chapters of "basic course.." on both fundamental group and classification of two manifolds, seemed like a playtime book.

homology theory is notoriously hard to make understandable, and i would suggest looking at books by fulton, and the chapter in spivak's differential geometry book vol 1, as well.

i also recommend massey's book on differential topology, first steps.

hocking and young is a very old fashioned book, which has much good classical material, but more on point set topology than you need in algebraic topology, and the point of view is not at all up to date.

all the professional algebraic topologists here love to use hatcher in their courses, but to me it is not that appealing. i liked vick, homology theory, as a student also.

spanier is very detailed and formidable, but excellent for those wishing to become professionals.

for beginners massey is hard to beat. if you read german there is also a fine book by artin and braun, which was apparently the model for the first part of greenberg's book.

- #16

xristy

Gold Member

- 116

- 2

Should be Wallace; "Differential Topology, First Steps"?i also recommend massey's book on differential topology, first steps.

Massey's "Basic Course..." is very nice indeed and almost certainly a better recommendation than Hocking and Young.

- Replies
- 10

- Views
- 3K

- Last Post

- Replies
- 5

- Views
- 5K

- Replies
- 8

- Views
- 7K

- Last Post

- Replies
- 5

- Views
- 3K

- Replies
- 1

- Views
- 3K

- Last Post

- Replies
- 3

- Views
- 10K

- Last Post

- Replies
- 3

- Views
- 6K

- Last Post

- Replies
- 3

- Views
- 3K

- Last Post

- Replies
- 4

- Views
- 9K

- Last Post

- Replies
- 4

- Views
- 11K