Configuration Spaces for the Working Undergraduate

TL;DR

This paper introduces configuration spaces and their algebraic topology to advanced undergraduates, covering Euclidean plane cases, braid groups, and graph configurations with accessible explanations.

Contribution

It provides an accessible introduction to configuration spaces and explores their properties in Euclidean spaces and graphs, including braid groups.

Findings

Configuration spaces of the Euclidean plane relate to braid groups.

Techniques for studying configuration spaces of graphs are discussed.

Accessible presentation for undergraduates is developed.

Abstract

Configuration spaces form a rich class of topological objects which are not usually presented to an undergraduate audience. Our aim is to present configuration spaces in a manner accessible to the advanced undergraduate. We begin with a slight introduction to the topic before giving necessary background on algebraic topology. We then discuss configuration spaces of the Euclidean plane and the braid groups they give rise to. Lastly, we discuss configuration spaces of graphs and the various techniques which have been developed to pursue their study.