Dominique Johannes: Simplicial Complexes and Alexander Duality
Tid: On 2018-09-05 kl 13.30 - 14.30
Plats: Room 22, House 5, Kräftriket, Department of Mathematics, Stockholm University  
Respondent: Dominique Johannes (BSc)
Handledare: Jörgen Backelin
Abstract: The purpose of this paper is to investigate properties of simplicial complexes and their Alexander duals. Concepts such as Stanley-Reisner ideals, Stanley-Reisner rings, chain complexes and homology for simplicial complexes are defined, and some important properties of these are discussed. Two types of resolutions, minimal free resolution and Taylor resolution, are constructed and used to compute Betti numbers of Stanley-Reisner rings. I also state the dual version of Hochster’s Formula, which uses Alexander duality to compute multigraded Betti numbers.