On the cohomology classes of planar polygon spaces

TL;DR

This paper derives an explicit formula for the cohomology classes of planar polygon spaces with fixed side lengths, which could impact understanding of their topological complexity.

Contribution

It provides a new explicit formula for the Poincare duality isomorphism in certain polygon spaces, advancing the mathematical understanding of their cohomology.

Findings

Explicit formula for Poincare duality isomorphism

Applicable to monogenic side length configurations

Potential implications for topological complexity

Abstract

We obtain an explicit formula for the Poincare duality isomorphism H^{n-3}(Mbar(ell)) to Z/2 for the space of isometry classes of n-gons with specified side lengths, if ell is monogenic in the sense of Hausmann-Rodriguez. This has potential application to topological complexity.