Equivariant Cayley Complex Embeddings

Abstract: In recent years, a lot of progress has been made in high-dimensional combinatorics, i.e. extending concepts from graph theory to higher dimensional CW-complexes. Two such concepts of particular interest are (i) group actions and (ii) embeddings. In this talk we will prove that every finite group which admits a faithful topological action over $\mathbb{S}^3$ has a generalised Cayley complex which embeds equivariantly in $\mathbb{S}^3$. In the process, we will see some recent theorems and lemmas concerning $2$-complex embeddings and group actions over $2$-complexes, and we will derive a new combinatorial characterization of finite groups acting faithfully and topologically over $\mathbb{S}^3$.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.