nLab equivariant formal group

Idea

A generalization of the concept of formal groups to a situation where an additional equivariance group acts.

In generalization of how formal groups correspond to complex oriented cohomology theories so equivariant formal groups correspond to equivariant complex oriented cohomology theories.

Properties

Universal equivariant formal group

Greenlees shows (Greenlees 01a, Greenlees 01b, Theorem 13.1 ) that the coefficient ring of equivariant complex cobordism theory classifies equivariant formal group laws over Noetherian rings, but the general conjecture is still open.

References

• Michael Cole, John Greenlees, Igor Kriz, Equivariant Formal Group Laws, Proceedings of the LMS, Volume81, Issue2 (2000)(doi:10.1112/S0024611500012466)

• John Greenlees, The coefficient ring of equivariant homotopical bordism classifies equivariant formal group laws over Noetherian rings, 2001 (preprint)

• John Greenlees, Multiplicative equivariant formal group laws, Journal of Pure and Applied Algebra Volume 165, Issue 2, 7 December 2001, Pages 183-200 (doi:10.1016/S0022-4049(00)00184-5)

• John Greenlees, Equivariant formal group laws and complex oriented cohomology theories, Homology Homotopy Appl. Volume 3, Number 2 (2001), 225-263 (euclid:hha/1139840255)

• Chun Lung Liu, Equivariant Algebraic Cobordism and Equivariant Formal Group Laws (arXiv:1305.2053)