# Questions tagged [algebraic-topology]

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.

12 questions
Filter by
Sorted by
Tagged with
41 views

### What is the correct domain of integration for the index of instantons? - $\mathbb{R}^4$ or $S^4$?

I posted the original question on Math SE but it seems like a more appropriate question for Physics SE: https://math.stackexchange.com/q/4417225/ In calculating the instanton solutions for $SU(2)$ ...
• 1,169
97 views

### Utility of Topological Data Analysis in Theoretical Physics

I audited a lecture on Topological Data Analysis, and I found it really interesting, primarily because of the connection to algebraic topology. I asked the professor if there are any connections to (...
• 2,855
69 views

• 1,956
144 views

### Large gauge transformation and intersection form

I am reading this paper and on pp.19-20 it states the following relation between large gauge transformation and intersection form: for the action on a 4-manifold $M^4$ S[A,B] = \int_{M^4}{\sum_{I=1}...
• 341
254 views

### Physical application of Postnikov tower, String$(n)$ and Fivebrane$(n)$

We know that the Spin group is quite a useful concept in physics. For example, Spin$(3)=SU(2)$ (and Spin$(6)=SU(4)$) that describe gauge groups in the Standard model and the isospin symmetry in the ...
• 7,430
### What is the importance of studying degeneration on $M_g$
Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$. It seems to be important in physics to study ... 