In this paper we first consider the Hamiltonian action of a compact connected Lie group on anH-twisted generalized complexmanifold M. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. If the generalized complex manifoldM satisfies the ∂∂-lemma, we prove that they are both canonically isomorphic to (Sg)⊗HH(M), where (Sg ) is the ...

We study an equivariant co-assembly map that is dual to the usual Baum–Connes assembly map and closely related to coarse geometry, equivariant Kasparov theory, and the existence of dual Dirac morphisms. As applications, we prove the existence of dual Dirac morphisms for groups with suitable compactifications, that is, satisfying the Carlsson–Pedersen condition, and we study a K–theoretic counte...

The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C2//Γ for cyclic Γ are studied using vertex operator technique, and connections between these rings and the class algebras of wreath products are explicitly established. We further show that certain generating functions of equivariant intersection numbers on the Hilbert schemes and related modul...

There is a natural evaluation map on the free loop space ΛX → Xk which sends a loop to its values at the kth roots of unity. This map is equivariant with respect to the action of the cyclic group on k elements Ck. We study the induced map in Ck-equivariant cohomology with mod two coefficients in the cases where k = 2m for m ≥ 1.

Fundamental and deep connections have been developed in recent years between the geometry of Hilbert schemes X [n] of points on a (quasi-)projective surface X and combinatorics of symmetric functions. Among distinguished classes of symmetric functions, let us mention the monomial symmetric functions, Schur polynomials, Jack polynomials (which depend on a Jack parameter), and Macdonald polynomia...

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier accessible. It is based on generalizing the notion of equivariance from lattices to point patterns of finite local complexity.

We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces of group actions. The importance of our enriched version of Moore’s theorem lies in its application to the construction of useful cochain alg...