Introduction to Computational Homology and Co-Homology

Alexandra Bac (LIS)

This session will focus on computational homology and co-homology. We will first briefly recall homology and co-homology definition (and insist on intuitions behind them), as well as "persistent homology" definition. Then we will present an overview on the question: "how to compute (co)homology and what do we expect"? Starting from this question, 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)