Hybrid Spaces with Interesting Cohomology

Loop Spaces of H-spaces with Finitely Generated Cohomology

Let p be an odd prime. We assume that all spaces are completed at p in the sense of Bousfield-Kan [2], and the cohomologies are taken with Z/pcoefficients unless otherwise specified. In this paper, we investigate the homotopy type for the loop space of an H-space whose cohomology is finitely generated as an algebra. In the case of the cohomology is finite dimensional, there is the following the...

Cohomology of Algebraic Spaces

Cohomology of Braid Spaces

where C+F(R9 p) denotes the singular chains of F(R , p), and Zp{q) denotes the Ip-module Zp with 2P-action a • x = ( l) x for xeZp and a e Zp ( ( 1) S(<T) is the sign of a). Since the Enaction on F(R, p) is proper, we may identify H*(HomEp(C^F(« , p) ; Zp(2g))) with H*(B(R ,p); Zp) [5]. By abuse of notation we denote H*(Hom2 ( Q F ^ p ) ; Zp(g))) by H*(B(R\p);Zp(q)). The interest in H*(B(R, p) ...

On Stringy Cohomology Spaces

We modify the definition of the families of A and B stringy cohomology spaces associated to a pair of dual reflexive Gorenstein cones. The new spaces have the same dimension as the ones defined in the joint paper with Mavlyutov [BoM], but they admit natural flat connections with respect to the appropriate parameters. This solves a longstanding question of relating GKZ hypergeometric system to s...

Cohomology of Moduli Spaces

Moduli spaces arise in classification problems in algebraic geometry (and other areas of geometry) when, as is typically the case, there are not enough discrete invariants to classify objects up to isomorphism. In the case of nonsingular complex projective curves (or compact Riemann surfaces) the genus g is a discrete invariant which classifies the curve regarded as a topological surface, but d...