Infinitesimal index: cohomology computations

TL;DR

This paper computes equivariant cohomology groups using the infinitesimal index, linking them to distribution spaces related to splines, with numerous improvements over previous versions.

Contribution

It introduces a method to compute equivariant cohomology via the infinitesimal index and distributions, enhancing previous approaches.

Findings

Explicit computations of equivariant cohomology groups.

Connection between cohomology and spline-related distributions.

Significant improvements over earlier versions.

Abstract

In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms of certain spaces of distributions arising in the theory of splines. The new version contains a large number of improvements.