URegina Topology and Geometry Seminar: Carlos Gabriel Valenzuela Ruiz

We continue last week’s talk by introducing two more combinatorial structures: simplicial and cubical complexes, which we’ll introduce and present some examples and constructions that arise from them. These complexes let us construct a family of Toric spaces we call moment-angle complexes. To study the homotopical features of these spaces we’ll introduce two algebraic objects which arise from the underlying simplicial complex: The Tor algebra and the Stanley-Reisner ring. Both encode the homological features of a MAC; we’ll present this equivalence, a proof sketch and some examples. If time permits, I’ll introduce polyhedral products and talk about some of the current work being done, such as the de-suspension problem and the triviality of the product.