ICTS:29091

Video URL

Property(T), median spaces and CAT(0) cubical complexes - 1

Property(T), median spaces and CAT(0) cubical complexes - 1

(2024). Property(T), median spaces and CAT(0) cubical complexes - 1. SciVideos. https://youtu.be/1_iooCz-TkU

Property(T), median spaces and CAT(0) cubical complexes - 1. SciVideos, Jul. 28, 2024, https://youtu.be/1_iooCz-TkU 

          @misc{ scivideos_ICTS:29091,
            doi = {},
            url = {https://youtu.be/1_iooCz-TkU},
            author = {},
            keywords = {},
            language = {en},
            title = {Property(T), median spaces and CAT(0) cubical complexes - 1},
            publisher = {},
            year = {2024},
            month = {jul},
            note = {ICTS:29091 see, \url{https://scivideos.org/icts-tifr/29091}}
          }
Indira Chatterji
Talk numberICTS:29091
Source RepositoryICTS-TIFR
Source EventGeometry in Groups
Collection

Abstract

I will give the basics on property(T), and explain the characterization in terms of actions on median spaces. I will discuss CAT(0) cubical complexes as examples of median spaces, and discuss groups acting on those objects as having a strong negation of property(T).
Possible problems for 2nd week:

Read ‘Spectral interpretations of property(T)’ by Yann Ollivier, with a generalization in mind. http://www.yann-ollivier.org/rech/publs/aut_spec_T.pdf
Study the orbits of the action of discrete cocompact subgroup P in SL^(2,R) on a median space (viewing P as a subgroup of the mapping class group of a surface prevents a proper action on a CAT(0) space). This will involve reading ‘Geometries of 3-manifolds’ by Peter Scott https://deepblue.lib.umich.edu/bitstream/handle/2027.42/135276/blms0401....

Pre-requisites: Bridson-Haefliger Part I, Part II Sections 1, 2 (ideally also 6,8,10), Part III H