# Kac-Moody Groups and Cosheaves on Davis Building

## TL;DR

This paper explores the representation theory of complete Kac-Moody groups through geometric methods, focusing on their action on Davis buildings and establishing key homological properties.

## Contribution

It introduces new geometric approaches to study Kac-Moody group representations, including projective dimension estimates and duality results.

## Key findings

- Estimate on projective dimension
- Localization theorem established
- Homological duality demonstrated

## Abstract

We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, localisation theorem, unimodularity and homological duality.