Summer School 2022 -  Cohomology, Geometry and Explicit number theory (COGENT)

Collection Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Organizer(s) Institut Fourier, CNRS, UGA
Date(s) 13/06/2022 - 30/06/2022
linked URL https://if-summer2022.sciencesconf.org/
00:00:00 / 00:00:00
44 55

Applications of twisted homology operations for E_n-algebras

By Calista Bernard

An E_n-algebra is a space equipped with a multiplication that is commutative up to homotopy. Such spaces arise naturally in geometric topology, number theory, and mathematical physics; some examples include classifying spaces of braid groups, spaces of long knots, and classifying spaces of general linear groups. The structure of an E_n-algebra gives rise to operations on the homology of a space, and these operations prove quite useful for studying homology. In the 70s F. Cohen and J.P. May gave a complete description of operations on the mod p homology of E_n-algebras, and more recently I have worked on generalizing their results to homology with twisted coefficients. In this talk I will give a brief introduction to E_n-algebras and the theory of operations, and I will then discuss work in progress on applications of this theory to studying the homology of special linear groups SL_n(Z) and to studying the twisted homology of mixed braid groups.

Information about the video

  • Date of recording 20/06/2022
  • Date of publication 03/12/2025
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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