nLab
B-bordism

Contemts

Contemts

Idea

A BB-bordism is a cobordism WW equipped with extra “topological structure” with respect to (B,f)-structure, i.e. in the form of a lift of the classifying map WBOW \to B O of its tangent bundle/stable normal bundle? through some fibration BBOB \to B O over the classifying space of the orthogonal group.

Commonly considered are lifts through the Whitehead tower of the orthogonal group), corresponding, in this order, to cobordisms with

etc.

Examples

flavors of bordism homology theories/cobordism cohomology theories, their representing Thom spectra and cobordism rings:

bordism theory\;M(B,f) (B-bordism):

relative bordism theories:

equivariant bordism theory:

global equivariant bordism theory:

algebraic:

References

Last revised on November 23, 2020 at 14:48:37. See the history of this page for a list of all contributions to it.