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Results tagged with at.algebraic-topology
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user 18702
Homotopy theory, homological algebra, algebraic treatments of manifolds.
46
votes
2
answers
4k
views
What are the potential applications of perfectoid spaces to homotopy theory?
This year's Arizona Winter School was on perfectoid spaces, and there were quite a few homotopy theorists in the audience. I'd like to get a "big list" of reasons homotopy theorists might care about p …
11
votes
0
answers
329
views
$K$-theory spectrum of the category of finite groups
(I asked some people this question in person and got the answer "no", but wanted to see if the Internet had more to say)$
\newcommand{\FinGrp}{\mathbf{FinGrp}}
$
Way back in my first group theory cou …
- 1,838
10
votes
2
answers
348
views
Affine spaces as algebras for an operad?
(at.algebraic-topology because I don't know who else thinks about operads)
Let $A$ be an affine space, i.e. a torsor over (the abelian group underlying) a vector space $V$ over a field $K$. Then for …
- 1,838
3
votes
What are the potential applications of perfectoid spaces to homotopy theory?
Edit Sep 2023: the ideas below have now been developed more thoroughly in my new paper Prisms and Tambara functors I
As Peter points out, it is more reasonable to look for connections between prisms …