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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Classification of higher Symmetry Protected Topological (SPT) phases
Suppose that we have a $d$ dimensional bosonic SPT phase, protected by some $p$-form symmetry, $G^{[p]}$. Suppose also that it is classified within group cohomology, so that we don't have to run into ...
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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 ...
JaP
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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 (...
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Reidemeister Torsion
Can somebody in a layman's language explain what is a Reidemeister Torsion? This seems to play an important role in path integral of 2+1-gravity as demonstrated here in arXiv:gr-qc/9406006. This is ...
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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 ...
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Are hierarchal states/fractional exchange statistics equivalent in the FQHE?
There are several theories for the fractional quantum Hall effect. The last listed in the Wikipedia article are composite fermions, though these seem to be a subset of fractional exchange statistics:
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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....
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