Stable cohomology of graph complexes in odd dimensions

TL;DR

This paper investigates the stable cohomology of graph complexes associated with configuration spaces and diffeomorphism groups of high-dimensional odd manifolds, extending previous work from even to odd dimensions.

Contribution

It provides the first computation of the stable cohomology for these graph complexes in odd dimensions, building on prior results in even dimensions.

Findings

Cohomology computed in the high genus limit

Extension of results from even to odd dimensions

New insights into configuration spaces and diffeomorphism groups

Abstract

We study graph complexes related to configuration spaces and diffeomorphism groups of highly connected manifolds of odd dimension. In particular we compute the cohomology in the "high genus" limit. This paper is a continuation of previous work by Felder, Naef and the second author in which the even dimensional case is studied.