Combinatorics Seminar

When: Sunday, November 27, 10am Where: Schreiber 309 Speaker: Eran Nevo, Hebrew University Title: Rigidity and a generalized g-conjecture

Abstract:

The g-theorem gives a complete characterization of the f-vectors of boundary complexes of simplicial polytopes (the f-vector counts the number of faces according to dimension). A long standing conjecture is that this characterization holds for all triangulated spheres. Recently Bjorner and Swartz conjectured that this characterization extends to the broader family of doubly Cohen-Macaulay complexes. We prove a small part of this conjecture, which, in particular, implies the following:

Barnette's lower bound theorem for f-vectors of simplicial polytopes extends to all doubly Cohen-Macaulay complexes.

For the proof we will need the concept of rigidity and Fogelsanger's concept of minimal cycle complexes.

All the needed technical terms will be defined in the talk!