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Results tagged with homotopy-theory
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user 18702
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.
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"Characteristics" (thick subcategories) in $n$-groupoids
$
\newcommand{\Ab}{\mathbf{Ab}}
\newcommand{\Sp}{\mathbf{Sp}}
$In 0-groupoids (sets), the thick subcategories of the category of abelian groups $\Ab$ are given by the primes $p$ and $0$, which we can …
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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 …
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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 …