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
(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
Parameterized (stable) homotopy theory is (stable) homotopy theory of bundles of homotopy types/stable homotopy types over a given base space.
For formalizations see at
Ioan Mackenzie James, Introduction to fibrewise homotopy theory in Ioan Mackenzie James (ed.), Handbook of Algebraic Topology (1995)
Peter May, J. Sigurdsson, Parametrized Homotopy Theory, 2006
Last revised on April 21, 2018 at 04:37:40. See the history of this page for a list of all contributions to it.