Date: 15 September 2017, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Ron Umble, Millersville University
   Title: Computing the cohomology algebra of a polyhedral complex

Abstract. The cohomology algebra of a space encodes topological
information not captured by its cohomology groups.  For example, the
cohomology groups of $S^1 \vee S^1 \vee S^2$ and $S^2 \times S^2$ are
isomorphic but their cohomology algebras are not.  Classically, one
computes the cohomology algebra of a space from the combinatorics of a
homeomorphic simplicial complex, but this can be computationally
inefficient.  In this talk we apply the transfer to merge the simplices
in a simplicial complex and obtain a polyhedral complex with fewer
cells.  Doing so simplifies the combinatorics and improves the
computational efficiency while preserving the algebraic topology.  We
show how to compute cup products directly from the combinatorics of the
resulting polyhedral complex.