cobordism theory = manifolds and cobordisms + stable homotopy theory/higher category theory
Concepts of cobordism theory
homotopy classes of maps to Thom space MO
complex cobordism cohomology theory
flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:
bordism theoryM(B,f) (B-bordism):
relative bordism theories:
global equivariant bordism theory:
algebraic:
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The 2-periodic version of complex cobordism cohomology theory MU is usually denoted (e.g. Lurie lecture 18, example 5).
may be realized as the Thom spectrum of the universal virtual complex bundle of arbitrary rank over the space (Lurie lecture 18, Example 5).
There is an analogue of the Landweber exact functor theorem for even 2-periodic cohomology theories, with MU replaced by MP (Lurie lecture 18, prop. 11).
flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:
bordism theoryM(B,f) (B-bordism):
relative bordism theories:
global equivariant bordism theory:
algebraic:
Last revised on September 23, 2021 at 11:22:05. See the history of this page for a list of all contributions to it.