# nLab MSpin^c

Contents

### Context

#### Cobordism theory

Concepts of cobordism theory

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:

algebraic:

# Contents

## Idea

The cobordism theory for manifolds equipped with (stable) Spin^c structure.

## Properties

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### Relation to complex K-theory

$M Spin^c$ 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:

algebraic:

## References

Created on February 18, 2021 at 09:53:45. See the history of this page for a list of all contributions to it.