String bordism

**cobordism theory** = manifolds and cobordisms + stable homotopy theory/higher category theory

**Concepts of cobordism theory**

**flavors of cobordism homology/cohomology theories and representing Thom spectra**

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$\,M B$ (B-bordism):

relative bordism theories:

global equivariant bordism theory:

algebraic:

Discussion of relation to the Witten genus:

- Carl McTague,
*The Cayley plane and String bordism*, Geom. Topol. 18 (2014) 2045-2078 (arXiv:1111.4520)

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

- Ulrich Bunke, Niko Naumann,
*Secondary Invariants for String Bordism and tmf*, Bulletin des Sciences Mathématiques, Volume 138, Issue 8, December 2014, Pages 912-970 (doi:10.1016/j.bulsci.2014.05.002)

Last revised on November 23, 2020 at 15:14:36. See the history of this page for a list of all contributions to it.