Combinatorics and topology of regular CW complexes
by
Patricia Hersh
North Carolina State University and Indiana University

Anders Björner characterized which finite, graded posets are closure posets of regular CW complexes, and he also observed that a regular CW complex is homeomorphic to the order complex of its closure poset. This suggests that one might use combinatorics to determine topological structure; however, it is possible for two different CW complexes with very different topological structure to have the same closure poset if one of them is not regular. I will talk about a new criterion for determining whether a particular finite CW complex is regular; this will involve an interplay of combinatorics and topology. I will review the notions from topology that we will need as well as the history of Björner's work and related work in this area.

Date received: February 15, 2009