Global group laws and equivariant bordism rings

Computations of complex equivariant bordism rings

We give explicit computations of the coefficients of homotopical complex equivariant cobordism theory MUG, when G is abelian. We present a set of generators which is complete for any abelian group. We present a set of relations which is complete when G is cyclic and which we conjecture to be complete in general. We proceed by first computing the localization of MUG obtained by inverting Euler c...

Geometric versus Homotopy Theoretic Equivariant Bordism

By results of Löffler and Comezaña, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G = S×. . .×S, we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of Sinha [22]. This is used in order to determine the image of the Pontrjagin-Thom map for toral G.

Computations in Complex Equivariant Bordism Theory

Equivariant Formal Group Laws and Complex Oriented Cohomology Theories

The article gives an introduction to equivariant formal group laws, and explains its relevance to complex oriented cohomol-ogy theories in general and to complex cobordism in particular.

Bordism, and Free Group Actions

In this paper we give characteristic class formulae for all semicharacteristic classes of all compact, closed manifolds with finite fundamental groups. These invariants are identified with elements in certain odd L-groups, and exactly which elements occur is specified. An appendix calculates the cohomology of the model groups needed. A second appendix determines the structure of the L-groups ne...