Configuration Spaces for the Working Undergraduate

zbMATH Open1462.55007arXiv1911.11186MaRDI QIDQ4965471

Lucas Williams

Publication date: 1 March 2021

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.

Full work available at URL: https://arxiv.org/abs/1911.11186

zbMATH Keywords

braid groupsconfiguration spaces of graphsgraph braid groupsnon-\(k\)-equal configurations

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes (57-01)

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