Finite group action and 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

Species with an equivariant group action

Joyal’s theory of combinatorial species provides a rich and elegant framework for enumerating combinatorial structures by translating structural information into algebraic functional equations. We also extend the theory to incorporate information about “structural” group actions (i.e. those which commute with the label permutation action) on combinatorial species, using the Γ-species of Henders...

Equivariant LS-category for finite group actions

In this paper we study the equivariant category of finite group actions. We introduce the basic filtration for the orbit space of the action. In terms of this filtration we give upper and lower estimates of the equivariant category. The idea for the proof is parallel to the approach in [3] for compact-Hausdorff foliations. We give examples to show that both the upper and lower bounds are realiz...