Topological complexity of spatial polygon spaces

TL;DR

This paper determines the topological complexity of the space of n-gons in three-dimensional space with fixed side lengths, showing it equals 2n-5 under certain conditions, using cohomology ring properties.

Contribution

It provides a precise calculation of the topological complexity for spatial polygon spaces based on their cohomology, extending understanding of their topological properties.

Findings

Topological complexity of spatial n-gon spaces is 2n-5.

The result applies when the space is nonempty and contains no straight-line polygons.

Uses known cohomology ring results to derive complexity.

Abstract

Using known results about their integral cohomology ring, we prove that the topological complexity of the space of n-gons in R^3 with prescribed side lengths equals 2n-5, assuming that the space is nonempty and does not contain any straight-line polygons.