Introduction to topological data analysis - Lecture 05

Persistent homology

The next step: applying topological invariants to geometric models

Simplicial homology

For $R=\mathbb{Z}$ and $R=\mathbb{Z}/2$ chains have a nice geometric interpretation:

Simplicial homology

For $R=\mathbb{Z}$ and $R=\mathbb{Z}/2$ chains have a nice geometric interpretation:

Simplicial homology

We are interested in cycles:

Simplicial homology

But how many cycles do we have?

Simplicial homology

But how many cycles do we have?