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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.

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4
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2answers
252 views

Simple explanation for what a torsor is

I am studying Chris Elliott's notes on Line and Surface Operators in Gauge Theories (available here). In the notes, there's a mention of the fact that (for $G = U(1)$), $$W_{\gamma, n}(A) = e^{in\...
3
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1answer
87 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}...
1
vote
2answers
112 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 ...
1
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0answers
68 views

String topology in string theory

How do string topology, string field theory and topological strings interact? Does anybody see a global picture? By string topology I mean the TQFT based on the homology of the space of loops ...
1
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0answers
57 views

Which geometry does not allow the existence of matter?

I have seen these lectures by Fredric Schuller that discuss the obstruction theory and the role of global geometric properties in admitting a spin structure. See the video at 01:27:52 https://youtu....
0
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0answers
16 views

Literature Anyons [duplicate]

In a few months I have to give a talk about Identical Particles in Quantum Physics, which should answer the following questions or explain following concepts: Why are there only Fermions and Bosons ...
0
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0answers
34 views

Connectedness on Special Kaehler manifolds

I just wanted to make a short/concise question which is quite mathematical but the aim is physical so I would like to ask it here. Anyone knows if there is a general statement about connectedness on ...