PIRSA:19100081 Scientific Series Mathematical physics

DOI10.48660/19100081

Series: Mathematical Physics

Chen, H. (2019). Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology. Perimeter Institute. https://pirsa.org/19100081

Chen, Harrison. Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology. Perimeter Institute, Oct. 24, 2019, https://pirsa.org/19100081 

@misc{ pirsa_PIRSA:19100081,
  doi = {10.48660/19100081},
  url = {https://pirsa.org/19100081},
  author = {Chen, Harrison},
  keywords = {Mathematical physics},
  language = {en},
  title = {Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology},
  publisher = {Perimeter Institute},
  year = {2019},
  month = {oct},
  note = {PIRSA:19100081 see, \url{https://pirsa.org}}
}

Abstract

There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights and new computational tools.  In the case of a quotient stack, we discuss a "Jordan decomposition" of loops which is made precise by an equivariant localization result.  We also discuss an Atiyah-Segal completion theorem which relates completed periodic cyclic homology to Betti cohomology.

 

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