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.

Author Bio

Lucas Williams is a senior math major at Reed College. He completed this work in the summer of 2019 and hopes to continue studying algebraic topology. Outside of mathematics he likes soccer, cooking, reading for pleasure, and listening to music.