homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
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see also algebraic topology
Introductions
Definitions
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Homotopy groups
Basic facts
Theorems
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
manifolds and cobordisms
cobordism theory, Introduction
Twisted Cohomotopy is the twisted cohomology-variant of the the non-abelian cohomology-theory Cohomotopy, represented by homotopy types of n-spheres.
The coefficients/twist for twisted Cohomotopy are spherical fibrations, and cocycles are sections of these. For those spherical fibrations arising as unit sphere bundles of real vector bundles the twist may be understood as given by the J-homomorphism.
Various classical theorem of differential topology are secretly theorems about twisted cohomotopy, including:
cohomology | equivariant cohomology | |
---|---|---|
non-abelian cohomology | cohomotopy | equivariant cohomotopy |
twisted cohomology | twisted cohomotopy | |
stable cohomology | stable cohomotopy | equivariant stable cohomotopy |
Discussion for twisted stable cohomotopy (framed cobordism cohomology theory):
Discussion of unstabilized twisted cohomotopy, with application to foundations of M-theory:
Last revised on June 19, 2019 at 04:27:29. See the history of this page for a list of all contributions to it.