Afshin Goodarzi:Higher dimensional analogues of Whitney theorem

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.