# Rachael Boyd: Embedding spaces of split links

**Time: **
Wed 2022-11-30 13.15

**Location: **
KTH, 3418

**Lecturer: **
Rachael Boyd (Cambridge University)

**Abstract**

This is joint work with Corey Bregman. We study the homotopy type of embedding spaces of unparameterised links, inspired by work of Brendle and Hatcher. We obtain a simple description of the fundamental group of the embedding space, which I will describe for you. Our main tool is a homotopy equivalent semi-simplicial space of separating spheres. As I will explain, this is a combinatorial object that provides a gateway to studying the homotopy type of embedding spaces of split links via the homotopy type of their individual pieces.