Graduate Seminar

Location:  RI 208 and Livestream

Speaker: Shashen Gounden

MSc Student supervised by Don Stanley

Title:  Multicomplexes, Generalized Davis-Januszkiewicz Spaces and Steenrod’s Realization Problem

Zoom: https://uregina-ca.zoom.us/j/92053635111?pwd=U25NcEp6amlGV1YrRDdnUm5qNlhaUT09

Abstract:

Multicomplexes are combinatorial objects that are generalizations of simplicial complexes. We follow the definition of a multicomplex introduced in Trevisan (2011) and show its correspondence with monomial ideal rings known as Stanley-Reisner rings, but unlike in the traditional construction with simplicial complexes these monomial rings are not square free. Following on from the work of Trevisan (2011) we construct the colimit over a multicomplex known as a Generalized Davis-Januszkiewicz space and we show that every monomial ring can be realized topologically by these spaces and extend the results of Trevisan (2011) to allow for generators of degree 2 and 4.