B. Benedetti, Shellings, local constructions and handle decompositions

Bruno Benedetti, Freie Universitat Berlin

Shellings, local constructions and handle decompositions.
 
A natural approach to study triangulated manifolds is to try
 and construct them `one piece at the time'. Variations of this idea have  been studied in different fields of math, and different epoques: from the  dawn of convex polytope theory ("shellings") to differential topology  ("handle decompositions"), from combinatorial commutative algebra  (Hochster's "constructions") to discrete quantum gravity
(Durhuus-Jonsson's "local constructions").  We compare these approaches and discuss connections with Morse theory, as
well as with its discretization by Forman.