分野別セミナー

A polyhedral product is a space combinatorially constructed from a collection of pairs of spaces and an abstract simplicial complex. This space originally appeared in an old paper of homotopy theory and is recently focused on in connection with toric topology. In this talk, we first review the connection between a polyhedral product and a combinatorics of its underlying simplicial complex. We then show a characterization of Golodness of a triangulated surface both in a combinatorial way and a topological way though polyhedral products, where Golodness is a combinatorial property of a simplicial complex defined by its Stanley-Reisner ring. The key is the fat wedge filtration of a polyhedral product introduced by Kouyemon Iriye and the speaker. We also present simplicial complexes which show dependence of Golodness on the ground ring. This is joint work with Kouyemon Iriye.