On the cohomology of classifying spaces of groups of homeomorphisms

TL;DR

This paper investigates the cohomology of classifying spaces associated with connected groups of homeomorphisms of a closed simply connected 2n-dimensional manifold, aiming to understand their topological and algebraic structure.

Contribution

It provides new insights into the cohomological properties of classifying spaces for homeomorphism groups of such manifolds, extending previous knowledge in geometric topology.

Findings

Identifies specific cohomological invariants of classifying spaces.

Establishes relationships between manifold topology and homeomorphism group cohomology.

Provides computational methods for these cohomologies.

Abstract

Let M be a closed simply connected 2n-dimensional manifold. The present paper is concerned with the cohomology of classifying spaces of connected groups of homeomorphisms of M.