Sumários
Simplicial Homology
8 Outubro 2024, 10:00 • Florian Pausinger
In this class we introduced simplicial homology. In particular, we defined chain-, cycle- and boundary groups and saw how they are related and used to define homology groups.
Convex set systems
1 Outubro 2024, 10:00 • Florian Pausinger
We studied the Nerve Theorem and saw how to relate a union of convex sets to its nerve. This technique is important whenever we try to use finite point samples to reconstruct a given compact space.
Moreover, we introduced two important types of simplicial complexes, namely the Cech-complex and the Vietoris Rips complex.