nLab
global equivariant bordism homology theory

Idea

The generalization of equivariant bordism homology theory (hence of bordism homology theory) to global equivariant homotopy theory.

Related concepts

• ultracommutative ring spectrum

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

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

• MFr

• MO, MSO, MSpin, MString, …

• MU, MSU, …

  MΩΩSU(n)

  MP, MR

• MSp

relative bordism theories:

• MOFr, MUFr, MSUFr

equivariant bordism theory:

• equivariant MFr

• equivariant MO

• equivariant MU

global equivariant bordism theory:

• global equivariant mO,

• global equivariant mU

algebraic:

• algebraic cobordism

References

• Stefan Schwede, Section 6 of: Global homotopy theory, New Mathematical Monographs 34, Cambridge University Press, 2018 (doi:10.1017/9781108349161, arXiv:1802.09382)

Survey:

• Stefan Schwede, Equivariant bordism from the global perspective, 2015 (pdf, pdf)