Contracting The Well-Rounded Retract

TL;DR

This paper introduces a method for contracting the well-rounded retract in low ranks, aiming for higher ranks, and applies it to compute cohomology groups, with future results anticipated.

Contribution

It presents a novel contraction method for the well-rounded retract in rank one and two, with plans to extend to higher ranks and applications in cohomology computations.

Findings

Method successfully contracts the well-rounded retract in low ranks

Application demonstrated in computing cohomology groups

Future work planned for higher rank generalizations

Abstract

In this paper we present a method for contracting the well-rounded retract in rank one and two, with a forward look to generalizing this approach in higher rank. We also present an application of this result in computing cohomology groups with coefficients, and announce forthcoming results in this field.