Topology of spaces of loops

Abstract: In my talk I will start with a brief introduction to configuration spaces and some basic results (e.g. the natural projection $PB_n\to PB_{n-1}$, by forgetting the $n$-th puncture, is known to be a fibration. This fact is no longer true for the pure untwisted rings/wickets). After that I want to explain the geometric method of Brendle and Hatcher, explained in their 2010 paper titled *Configuration Spaces of Rings and Wickets* for computing some of the fundamental groups and demonstrate this on some examples. There is, however, a limitation of this procedure, i.e. the method does not imediately apply to *pure untwisted wickets*. In the last part of my talk I will point out this problem and indicate a (hopefully possible) solution to this, which (if it works out) in the end will be some of my results of my master thesis.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

Göttingen topology and geometry seminar

Series comments: Our seminar takes place via zoom every Tuesday afternoon (Central European Summer Time; the precise time slot varies—please always refer to the listing).