homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
group cohomology, nonabelian group cohomology, Lie group cohomology
Hochschild cohomology, cyclic cohomology?
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
This entry collects links related to the book
Parametrized Homotopy Theory,
Mathematical Surveys and Monographs 132
AMS 2006
on parameterized stable homotopy theory, hence on stable homotopy theory in slice (infinity,1)-toposes Top$/X$ for given topological base spaces $X$: the homotopy theory of ex-spaces and parametrized spectra.
A survey is in the slides
Beware that section 4.4 claims a new proof of the Strøm model structure, but relying on
which later was noticed to be false, by Richard Williamson; for details see p. 2 and Rem 5.12 and Sec. 6.1 in:
One application is twisted cohomology: instead of cocycles given by maps $X \to A$, twisted cocycles are given by sections $X \to P$ of a bundle $P \to X$ of spectra over $X$.
A discussion of some of these issues using tools from (infinity,1)-category theory are in
See also
A general abstract context for parameterized spectra are tangent (infinity,1)-toposes.
Last revised on September 20, 2021 at 05:34:33. See the history of this page for a list of all contributions to it.