Differential geometry of the space of orbits of a Coxeter group

TL;DR

This paper explores the differential geometry of the orbit space of finite Coxeter groups, using Grothendieck residues to construct a 2D topological field theory applicable to any Coxeter group.

Contribution

It introduces a differential-geometric framework for Coxeter group orbit spaces and constructs a corresponding 2D topological field theory, expanding the mathematical understanding of these structures.

Findings

Calculated differential-geometric structures using Grothendieck residues

Constructed a 2D topological field theory for arbitrary Coxeter groups

Provided new insights into the geometry of Coxeter group orbit spaces

Abstract

Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group.