Localizing equivariant bordism

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 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...

Computations in Complex Equivariant Bordism Theory

The Geometry of the Local Cohomology Filtration in Equivariant Bordism

We present geometric constructions which realize the local cohomology filtration in the setting of equivariant bordism, with the aim of understanding free G actions on manifolds. We begin by reviewing the basic construction of the local cohomology filtration, starting with the Conner-Floyd tom Dieck exact sequence. We define this filtration geometrically using the language of families of subgro...

Real Equivariant Bordism and Stable Transversality Obstructions for Z/2

In this paper we compute homotopical equivariant bordism for the group Z/2, namely MO Z/2 ∗ , geometric equivariant bordism N Z/2 ∗ , and their quotient as N Z/2 ∗ modules. This quotient is a module of stable transversality obstructions, closely related to those of [4]. In doing these computations, we use the techniques of [7]. Because we are working in the real setting only with Z/2, these tec...