# nLab String bordism

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

String bordism theory, $MString$, is bordism homology theory for manifolds equipped with string structure.

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

Discussion of relation to the Witten genus:

Discussion of secondary characteristic classes in string cobordism cohomology theory and in tmf:

String bordism of the classifying space of $E_8$:

• Michael Hill, The $String$ bordism of $B E_8$ and $B E_8 \times B E_8$ through dimension 14, Ill. J. Math. 53 1 (2009) 183-196 [doi:10.1215/ijm/1264170845]

Discussion of geometric string bordism in degreee 3 as a means to speak (via the Pontryagin-Thom theorem) about the third stable homotopy group of spheres:

Last revised on March 16, 2023 at 10:27:45. See the history of this page for a list of all contributions to it.