Homology and Fundamental Group Algorithms via Forman's Discrete Morse Theory

Thursday, February 13, 2014 - 11:30am - 12:20pm
Keller 3-180
Marian Mrozek (Jagiellonian University)
Efficient algorithmic computation of homology groups and the fundamental
group of a subset of Euclidean space is among the basic problems
in present-day Applied Topology. Particular interest is in algorithms
taking finite CW complexes on input. At the end of 20th century
Robin Forman proposed a version of the classical
Morse theory for a CW complex embedded with a combinatorial counterpart of
a vector field. In the talk we will demonstrate how this theory may be
fruitfully used in the construction of homology algorithms.
We will also show a recent extension of this approach to the algorithmic
computation of a presentation of the fundamental group.
MSC Code: