# Afshin Goodarzi:Mixed connectivity for cell complexes

**Time: **
Wed 2021-01-20 14.15 - 15.15

**Location: **
Zoom meeting ID: 654 5562 3260

Abstract: The classical Steinitz's theorem (1922) asserts that a graph is the 1-skeleton of a convex 3-polytope if and only if it is 3-connected and planar. In 1961, Balinski extended the "only if" direction of Steinitz's theorem by showing that the 1-skeleton of a convex d-polytope is d-connected.

In this talk, which is based on a joint work with Anders Björner, some results that combine k-connectivity of graphs and topological k-connectivity of spaces will be presented.

In particular, it will be shown that if we remove some d-k vertices (and all faces containing them) from the k-skeleton of the boundary of a convex d-dimensional polytope, then the remaining complex is topologically (k-1)-connected. This extends the result of Balinski (the k = 1 case).

Zoom link: https://kth-se.zoom.us/j/65455623260

Zoom meeting ID: 654 5562 3260