### Some Computational Homology Lectures

Slides of a lecture on computational homology
delivered at the Dynamics,Topology and Computations conference in Bedlewo,
Poland, 24-30 June 2012.

And below are slides of a 4-lecture mini course given at the Summer
School in Algorithmic
Mathematics, FU Berlin, August 16-20, 2010

Lecture 1:
Persistent homology and some applied topology

Lecture 2:
Discrete Morse Theory, homology computation and the homology of finite
groups

Lecture 3:
Perturbation Lemma, homology of some crystallographic and arithmetic
groups, and the K(pi,1)-conjecture for Artin groups

Lecture 4: A
higher dimensional Seifert-van Kampen theorem and the homotopy groups
of the 2-sphere