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
and have experience in some aspects of writing code for these
will have encountered some other interesting applications of
Simplicial complexes, abstract and geometric.
Collapsing and graph evasivenes.
Other kinds of complex:
Čech, convex set complexes, Vietoris-Rips,
Homology groups. Motion of objects in contact
(Hopcroft and Wilfong). Concrete methods of calculating
Persistent homology groups and their calculation.
Some graph-theoretic and related algorithms will be introduced
and used where needed.
MA3428 (Algebraic Topology II), knowledge of C or C++ programming.
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.
Edelsbrunner and Harer. Computational Topology: an Introduction. The chapters on graphs, complexes, homology, Morse functions, and persistence,
will be used.