nLab equivariant cobordism theory

Idea

The generalization of cobordism theorem to equivariant homotopy theory/equivariant differential topology.

Theorems

• equivariant Pontrjagin theorem

• (…)

Related concepts

• Real cobordism cohomology

• differential cobordism cohomology

• equivariant differential topology

• equivariant homotopy theory, equivariant stable homotopy theory

• equivariant cohomology

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

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

• MFr

• MO, MSO, MSpin, MString, …

• MU, MSU, …

  MΩΩSU(n)

  MP, MR

• MSpin^c

• 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

For more see at the references at equivariant bordism homology theory.

• Po Hu, Igor Kriz, Yunze Lu, Coefficients of the $\Sigma_3$-equivariant complex cobordism ring [arXiv:2109.00991]

Review in global equivariant homotopy theory:

• Ningchuan Zhang, Equivariant cobordism (2019) [pdf]