nLab MSpinᶜ

Contents

Contents

Idea

The cobordism theory for manifolds equipped with (stable) spinᶜ structure.

Properties

Atiyah-Bott-Shapiro orientation

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see at Atiyah-Bott-Shapiro orientation

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Relation to complex K-theory

MSpin cM Spin^c is related to KU in a variant of the Conner-Floyd isomorphism, via the Atiyah-Bott-Shapiro orientation (Hopkins-Hovey 92, Thm. 1)

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 July 5, 2024 at 14:11:57. See the history of this page for a list of all contributions to it.