Introduction to Computational Homology and Co-Homology - Part 2

Alexandra Bac (LIS)

Previous session has focussed on the definition and illustration of objects handled by homology and co-homology (and insisting on intuitions behind them), as well as "persistent homology" definition.

In this second session, starting from the question: "how to compute (co)homology and what do we expect ?", we will show that (co)homology can be computed "at different levels". And we will introduce state-of-art approaches for computing homology and persistent homology:

• Algebraic approach (Smith Normal Form)
• Categorical approach (effective homology)
• Combinatorial approach (Discrete Morse Theory)
• Made in Marseile: Homological Discrete Vector Fields or HDVF (encompasses previous approaches)