Polynomial Assignments

TL;DR

This paper demonstrates that the equivariant cohomology ring of a manifold can be largely determined by combinatorial data from the infinitesimal orbit-type stratification, advancing understanding of group actions on manifolds.

Contribution

It answers a question from prior work by showing the significant influence of combinatorial data on the equivariant cohomology ring.

Findings

Equivariant cohomology ring is largely determined by infinitesimal orbit-type stratification data.

Provides a positive answer to a previously posed question in the field.

Enhances methods for extracting geometric information from combinatorial data.

Abstract

The concept of assignments was introduced in [GGK99] as a method for extracting geometric information about group actions on manifolds from combinatorial data encoded in the infinitesimal orbit-type stratification. In this paper we will answer in the affirmative a question posed in [GGK99] by showing that the equivariant cohomology ring of $M$ is to a large extent determined by this data.