# Afshin Goodarzi:Higher dimensional analogues of Whitney theorem

**Time: **
Wed 2023-05-24 10.15 - 11.15

**Location: **
KTH 3721

**Participating: **
Afshin Goodarzi (KTH)

Abstract: An ear decomposition of a graph G is an ordered set of paths such that the first path is closed (i.e., is a cycle) and every other path is glued to the union of all previous paths at two distinct points from its end-points. A classical theorem by Hassler Whitney (1932) states that a graph G has an ear decomposition if and only if it is 2-connected. Considering a graph as a 1-dimensional simplicial complex, in this talk, I discuss various possible higher dimensional analogues of ear decomposition and graph-theoretic 2-connectivity by emphasizing on the concepts such as normality, Cohen–Macaulayness and their relatives. In particular, I present a 2-dimensional analogue for Whitney's theorem.