will be familiar with the practical aspects of homology theory;

will be familiar with abstract and concrete simplicial complexes;

will be able to calculate some homology groups and persistent homology
groups,
and have experience in some aspects of writing code for these
calculations;

will have encountered some other interesting applications of
(algebraic) topology.

Module Content

Simplicial complexes, abstract and geometric.

Collapsing and graph evasivenes.

Other kinds of complex:
Čech, convex set complexes, Vietoris-Rips,
Delaunay, alpha.

Homology groups. Motion of objects in contact
(Hopcroft and Wilfong). Concrete methods of calculating
homology groups.

Persistent homology groups and their calculation.

Some graph-theoretic and related algorithms will be introduced
and used where needed.

Module Prerequisite

MA3428 (Algebraic Topology II), knowledge of C or C++ programming.

Assessment Detail

This module will be examined
in a 2-hour examination in Trinity term.
There will be fortnightly quizzes and some
programming assignments. The overall mark will
be 80% exam, 10% quizzes, and 10% programming.

Text

Edelsbrunner and Harer. Computational Topology: an Introduction. The chapters on graphs, complexes, homology, Morse functions, and persistence,
will be used.