Combinatorial topology and group theory (University of Pisa, Fall 2021)

This mini-course consists of 5 lectures of 2 hours each. Important announcements will appear here and in the mailing list.

Language: English

Schedule

1. Partially ordered sets [notes]
   Tuesday, Nov 23, 16:00-18:00
2. Cell complexes, discrete Morse theory [notes]
   Thursday, Nov 25, 16:00-18:00
3. Examples for discrete Morse theory; introduction to Garside structures [notes]
   Tuesday, Nov 30, 16:00-18:00
4. Combinatorial Garside structures, Garside monoids [notes] [proof of lemma 1]
   Friday, Dec 3, 16:00-18:00
5. Garside monoids and Garside groups: normal form and classifying spaces [notes]
   Tuesday, Dec 7, 16:00-18:00

All notes: ctgt2021.pdf

Bibliography

• Armstrong, Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
• Batzies, Discrete Morse Theory for Cellular Resolutions
• Björner-Brenti, Combinatorics of Coxeter groups
• Brown, Topology and Groupoids
• Charney-Meier-Whittlesey, Bestvina's normal form complex and the homology of Garside groups
• Dehornoy, Groups with a complemented presentation
• Dehornoy-Digne-Godelle-Krammer-Michel, Foundations of Garside Theory
• Dehornoy-Paris, Gaussian groups and Garside groups, two generalisations of Artin groups
• Forman, Morse Theory for Cell Complexes
• Hatcher, Algebraic Topology
• Kozlov, Combinatorial Algebraic Topology
• McCammond, An Introduction to Garside Structures
• Stanley, Enumerative Combinatorics
• Wachs, Poset Topology: Tools and Applications