September 8, 2010
Bruno Benedetti, TU Berlin: Counting manifolds via discrete Morse theory
Abstract:
A crucial issue in lattice gravity is to control the number of
triangulations of manifolds, at least asymptotically. Typically, one
counts the number of different combinatorial types with respect to the
number N of facets. For example, in two dimensions, there are
exponentially many surfaces with bounded genus. Unfortunately, little
is known about higher dimensions. How many 3-spheres are there? Which
parameters should we restrict in order to achieve exponential bounds
on 3-, or 4-manifolds? We will show how Forman's discrete Morse theory
provides a new perspective for these problems.