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Results tagged with homotopy-theory
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user 6074
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
38
votes
Analogue to covering space for higher homotopy groups?
My apologies for coming back to this old question, but I want to address a point that I think is not really addressed so far. Namely, for $n=1$, the universal cover of a (reasonable) topological space …
- 21.3k
5
votes
Accepted
Domain of left adjoint from condensed sets to anima
Great question!
The answer is Yes. Let me elaborate a little. The question is more generally about the left adjoint to the inclusion $\mathrm{An}\to \mathrm{CondAn}$ from anima to condensed anima. Thi …
- 21.3k
28
votes
Accepted
What is the precise relationship between pyknoticity and cohesiveness?
The work on analytic geometry is all joint with Dustin Clausen!
Your main question seems a little vague to me, but let me try to get at it by answering the subquestions. See also the discussion at th …
- 21.3k
18
votes
What are the potential applications of perfectoid spaces to homotopy theory?
Good question!
Actually, it seems unlikely that perfectoid methods per se play a key role in homotopy theory. The reason is that perfectoid things are "infinitely ramified", but there are theorems to …