In this paper we construct a bivariant Chern character for the equivariant KK-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes conjecture for a totally disconnected group is isomorphic to cosheaf homology. Moreover, it is shown that our transfo...

Assume (M,ω) is a connected, compact 6 dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case dim H(M) < 3. We give a complete list of the possible manifolds, determine their equivariant cohomology ring and equivariant Chern classes. Some of t...

We introduce a mutation algorithm for puzzles that is a threedirection analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. Thanks...