Geometric presentation for the cohomology ring of polygon spaces

TL;DR

This paper presents two computationally friendly geometric descriptions of the cohomology ring of polygon spaces, enabling easier calculations of their algebraic structure.

Contribution

It introduces two new presentations of the cohomology ring that are both geometrically meaningful and computationally simple.

Findings

Two new presentations of the cohomology ring are proposed.

The presentations allow straightforward computation of cup products.

The work enhances understanding of the algebraic structure of polygon spaces.

Abstract

We describe the cohomology ring of the moduli space of a flexible polygon in geometrically meaningful terms. We propose two presentations, both are computation friendly: there are simple rules for cup product.