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, MSpin^c, MSpin^h MString, MFivebrane, M2-Orient, M2-Spin, MNinebrane (see also pin⁻ bordism, pin⁺ bordism, pinᶜ bordism, spin bordism, spinᶜ bordism, spinʰ bordism, string bordism, fivebrane bordism, 2-oriented bordism, 2-spin bordism, ninebrane bordism)

• MU, MSU, MΩΩSU(n)

• MP, MR

• MSp

• MTO, MTSO

• 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]