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Vietoris-Rips Complexes and Geometric Group Theory

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Geometric Group Theory Courses Algebraic Topology Courses Hyperbolic Groups Courses Vietoris-Rips Complexes Courses

Course Description

Overview

Explore the role of Vietoris-Rips complexes in geometric group theory and their impact on studying topological finiteness properties of groups in this 51-minute talk. Delve into Rips' famous proof of eventual contractibility of Vietoris-Rips complexes in hyperbolic groups, demonstrating their geometric actions on contractible complexes. Examine Alonso's use of these complexes to establish quasi-isometry invariance of finiteness properties type FP_n and F_n. Discover recent Morse theoretic techniques for proving contractibility in more general groups and spaces, including implications for asymptotically CAT(0) groups. Investigate the connection between type FP_n finiteness properties and the (non-)persistent homology of Vietoris-Rips complexes, highlighting an area ripe for further exploration in group theory.

Syllabus

Matthew Zaremsky (5/21/21): Vietoris-Rips complexes and geometric group theory


Taught by

Applied Algebraic Topology Network

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