Homological stability for Temperley-Lieb algebras
Ponente: Rachael Boyd
Institución: Max Planck Institute
Tipo de Evento: Investigación
Institución: Max Planck Institute
Tipo de Evento: Investigación
Many sequences of groups and spaces satisfy a phenomenon called 'homological stability'. I will present joint work with Hepworth, in which we abstract this notion to sequences of algebras, and prove homological stability for the sequence of Temperley-Lieb algebras. The proof uses a new technique of 'inductive resolutions', to overcome the lack of flatness of the Temperley-Lieb algebras. I will also introduce the 'complex of planar injective words' which plays a key role in our work. Time permitting, I will explore some connections to representation theory and combinatorics that arose from our work. I will aim this talk at a broad topological audience, and assume no prior knowledge of homological stability or Temperley-Lieb algebras.