Homological stability for the Temperley-Lieb algebras

Rachael Boyd (Max Planck Institute, Bonn)

Monday 1st February 16:00-17:00 Online

Abstract

 

Many sequences of groups and spaces satisfy a phenomenon called 'homological stability'. In recent work with Hepworth, we abstract this notion to algebras and prove homological stability for the sequence of Temperley-Lieb algebras. This involves introducing new techniques to the standard framework for proving homological stability. As a result we show that 'stably'  the Tor groups over the 'trivial' representation vanish in a range (which depends on the ground ring). The main hurdle in such a proof is showing that a particular complex is highly connected. In our case, we introduce the 'complex of planar injective words', which I will define. I will also highlight the interplay between our result and the Jones-Wenzl projectors, which knot theorists and representation theorists may find interesting.
I will aim this talk at a broad topological audience, and assume no prior knowledge of homological stability or Temperley-Lieb algebras.


The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).


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