ICTS:29089

Video URL

Examples of infinite groups, their ℓ2-homology and boundaries - 1

Examples of infinite groups, their ℓ2-homology and boundaries - 1

(2024). Examples of infinite groups, their ℓ2-homology and boundaries - 1. SciVideos. https://youtu.be/OtxD_0RikaU

Examples of infinite groups, their ℓ2-homology and boundaries - 1. SciVideos, Jul. 29, 2024, https://youtu.be/OtxD_0RikaU 

          @misc{ scivideos_ICTS:29089,
            doi = {},
            url = {https://youtu.be/OtxD_0RikaU},
            author = {},
            keywords = {},
            language = {en},
            title = {Examples of infinite groups, their l2-homology and boundaries - 1},
            publisher = {},
            year = {2024},
            month = {jul},
            note = {ICTS:29089 see, \url{https://scivideos.org/icts-tifr/29089}}
          }
Genevieve Walsh
Talk numberICTS:29089
Source RepositoryICTS-TIFR
Source EventGeometry in Groups
Collection

Abstract

We will study groups acting geometrically on infinite polyhedral complexes. A good example to think of is the fundamental group of a surface Sg acting on the universal cover of a triangulated Sg. We will define, discuss, and state some properties of two very useful invariants of these spaces/actions: the ℓ2-homology of the space and the (Gromov) boundary of the space when it is hyperbolic. There will be many examples, which will hopefully lead to some intuition about these invariants. Possible second week problem based on Matt Clay’s paper ‘ℓ2-homology of the free group’.

Pre-requisites: Background that might be helpful includes some topology and covering space theory (for example Hatcher chapter 1), familiarity with simplicial homology, CW complexes, geometry of H2.