Let G = Zp, p a prime (resp. S1), act freely on a finitistic space X with mod p (resp. rational) cohomology ring isomorphic to that of Sm×Sn. In this paper we determine the possible cohomology algebra of the orbit space X/G.

The natural transformation Ξ from L–theory to the Tate cohomology of Z/2 acting on K–theory (constructed in [WW2] and [WWd]) commutes with external products. Corollary: The Tate cohomology of Z/2 acting on the K–theory of any ring with involution is a generalized Eilenberg–MacLane spectrum, and it is 4–periodic.

Let the reductive group G act on the finitely generated commutative k-algebra A. We ask if the finite generation property of the ring of invariants extends to the full cohomology ring. We confirm this when the action on A is replaced by the ‘contracted’ action on the Grosshans graded ring grA, provided the characteristic of k is large.

The λ-ring cohomology, H λ and H 1 λ, of certain truncated polynomial filtered λ-rings are computed.

We introduce K-theoretic versions of the Fantechi-Goettsche ring of a variety with a group action and the Chen-Ruan cohomology of a smooth complex orbifold which we call stringy K-theory. Our definition is a generalization of a construction due to Givental and Y. P. Lee and it differs from the orbifold K-theory of Adem-Ruan. We also introduce a stringy Chern character isomorphism Ch taking stri...

We prove a general formula for the intersection form of two arbitrary monomials in boundary divisors. Furthermore we present a tree basis of the cohomology of M0n. With the help of the intersection form we determine the Gram matrix for this basis and give a formula for its inverse. This enables us to calculate the tensor product of the higher order multiplications arising in quantum cohomology ...

We exploit the Fedosov-Weinstein-Xu (FWX) resolution proposed in q-alg/9709043 to establish an isomorphism between the ring of Hochschild cohomology of the quantum algebra of functions on a symplectic manifold M and the ring H(M,C((~))) of De Rham cohomology of M with the coefficient field C((~)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket ...

Let S = k[x1, . . . , xn] be a polynomial ring over a field k with n variables x1, . . . , xn, m the irrelevant maximal ideal of S, I a monomial ideal in S and I ′ the polarization of I in the polynomial ring S′ with ρ variables. We show that each graded piece H i m (S/I)a, a ∈ Z , of the local cohomology module H i m (S/I) is isomorphic to a specific graded pieceH i+ρ−n m ′ (S′/I )α, α ∈ Z , o...

Kumar described the Schubert classes which are the dual to the closures of the Bruhat cells in the flag varieties of the Kac-Moody groups associated to the infinite dimensional KacMoody algebras [17]. These classes are indexed by affine Weyl groups and can be chosen as elements of integral cohomologies of the homogeneous space L̂polGC/B̂ for any compact simply connected semisimple Lie groupG. Lat...

The face ring of a simplicial complex modulo m generic linear forms is shown to have finite local cohomology if and only if the link of every face of dimension m or more is nonsingular, i.e., has the homology of a wedge of spheres of the expected dimension. This is derived from an enumerative result for local cohomology of face rings modulo generic linear forms, as compared with local cohomolog...