Explicit Betti numbers for a family of nilpotent Lie algebras

Betti numbers for the Heisenberg Lie algebras were calculated by Santharoubane in his 1983 paper. However few other examples have appeared in the literature. In this note we give the Betti numbers for a family of -dimensional 2-step nilpotent extensions of by .

     

Equivariant acyclic maps

In this paper we apply a recently developed new version of the Bredon-Illman cohomology theory to obtain an equivariant analogue of a result of Kan and Thurston, which implies that a connected CW-complex has the homotopy type of a space obtained by applying the plus construction of Quillen to certain Eilenberg-MacLane spaces.

     

On The Homotopy Type of

We consider the homotopy type of classifying spaces , where is a finite -group, and we study the question whether or not the mod cohomology of , as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of . This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of .

     

Unramified cohomology and Witt groups of anisotropic Pfister quadrics

The unramified Witt group of an anisotropic conic over a field , with , defined by the form is known to be a quotient of the Witt group of and isomorphic to . We compute the unramified cohomology group , where is the three dimensional anisotropic quadric defined by the quadratic form over . We use these computations to study the unramified Witt group of .

     

Schubert cycles, differential forms and D-modules on varieties of unseparated flags

Proper homogeneous G-spaces (where G is semisimple algebraic group) over positive characteristic fields k can be divided into two classes, the first one being the flag varieties G/P and the second one consisting of varieties of unseparated flags (proper homogeneous spaces not isomorphic to flag varieties as algebraic varieties). In this paper we compute the Chow ring of varieites of unseparated flags, show that the Hodge cohomology of usual flag varieties extends to the general setting of proper homogeneous spaces and give an example showing (by geometric means) that the D -affinity of Beilinson and Bernstein fails for varieties of unseparated flags.     

Prime Submodules and a Sheaf on the Prime Spectra of Modules

We define and investigate a sheaf of modules on the prime spectra of modules, and it is shown that there is an isomorphism between the sections of this sheaf and the ideal transform module.     

Isolated complex singularities and their CR links

In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Floer–Novikov cohomology and the flux conjecture

We study Floer–Novikov cohomology with local coefficients and prove the flux conjecture for general closed symplectic manifolds. Received: February 2005, Revised: May 2006, Accepted: May 2006 Partially supported by the Grant-in-Aid for Scientific Research No. 14003419, Japan Society for the Promotion of Sciences.