Higher order cohomology of arithmetic groups

TL;DR

This paper explores higher order cohomology of arithmetic groups, linking it to (g,K)-cohomology and automorphic forms, and proposes a higher order version of Borel's conjecture for computing cohomology.

Contribution

It generalizes Borel's results by expressing higher order cohomology in terms of (g,K)-cohomology and formulates a new conjecture relating it to automorphic forms.

Findings

Cohomology can be computed via functions of moderate growth.

Higher order Borel conjecture is proposed.

Connections between cohomology and automorphic forms are established.

Abstract

Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of Borel's conjecture is stated, asserting that the cohomology can be computed using automorphic forms.