2
votes
4answers
274 views

Should I read about Manifolds or Algebraic Topology?

I really enjoy doing maths and it fills quite a lot of my spare time. I'm starting my first year in the university on october and I probably won't have that much time for independent reading once ...
2
votes
1answer
40 views

Good resource for learning braid theory?

I recently heard about braid theory and read the Wikipedia article on it, and it seems really beautiful. What is a good resource for learning more about it? I have a background in mathematics at the ...
8
votes
0answers
151 views

Am I reading Bott - Tu right?

Summary: I'm finding Bott - Tu to be too brief and terse. I constantly have to look elsewhere to fill in details. This is not time-efficient. Am I missing something? If not - what other books do ...
3
votes
1answer
44 views

Isomorphism of Grassmannians

I want to prove that two CW complexes $\mathrm{Gr}_{n}(\mathbb{R}^{n+k})$ and $\mathrm{Gr}_{k}(\mathbb{R}^{n+k})$ are isomorphic to one another. I'm pretty sure I can just show that the number of ...
0
votes
0answers
42 views

How to deform a curve in specific manner

I am wondering whether we can deform a path in specific ways continuously i mean if there is a closed piece wise $C^1$ smooth path which has to be deformed to another piece wise $C^1$ smooth path. Let ...
2
votes
1answer
83 views

How to prove that two curves are not path homotopic

I have a unit circle around origin.And another unit circle around $(2,0)$. Consider the domain $R^2 / \{(0,0)\}$. I am able to clearly see that both are not homotopic but i am unable to prove it ...
14
votes
7answers
468 views

Introduction to ring theory?

I've been teaching myself algebra these couple of months. I already went through the basics of group (Lagrange, action, class equation, Cauchy and Sylow theorems etc.) And I already have some linear ...
10
votes
1answer
298 views

Preparing for “differential forms in algebraic topology”?

I'd very much like to read "differential forms in algebraic topology". Apart from background in calculus and linear algbra I've thoroughly went through the first 5 chapters of Munkres. I'm thinking ...
5
votes
1answer
127 views

Prerequisites for bredon's “Topology and Geometry”?

My background in topology is the first 6 chapters of Munkres's "topology" and in algebra Herstein's "topics in algebra". Both of them I self studied. A look at the table of contents of bredon's ...
3
votes
2answers
416 views

Books for algebraic geometry, algebraic topology [duplicate]

Possible Duplicate: (undergraduate) Algebraic Geometry Textbook Recomendations I am planning to self-study one of these two subjects: Algebraic geometry , Algebraic topology. I can borrow ...
2
votes
1answer
161 views

Easy papers on fundamental groups (for beginners)

I'd like to read some papers concerning fundamental groups, for example, papers written to explain some basic facts about homotopy explicitly for undergraduate students. All the papers I have ...
0
votes
3answers
220 views

Algebraic Topology pamphlets?

I'm looking to self-learn some Algebraic Topology and have found the books I've looked at so far (ie. Hatcher) to be rather tome-like for my tastes. Does anyone know of a good slim lecture notes style ...
4
votes
1answer
281 views

Approach to Learning Co/Homology

I have decided to begin studying co/homology and I'm trying to work out the best approach to doing this. As I understand the situation, any system that satisfies the Eilenberg-Steenrod axioms ...
3
votes
2answers
301 views

study topology: homotopy and homology

I want to study the basis of topology. I know functional analysis and very basic topology. I need to learn about homologies and homotopies but it seems that all the books (mostly of Russian authors) ...
2
votes
1answer
251 views

Group acting on locally finite tree

Let $G$ be a group acting on a locally finite connected tree $T$ i.e. each vertex degree is finite. Let $G$ has compact open topology i.e. for each compact set $C$ and an open set $U$ of $T$, the sets ...