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SUMMARY:Loop spaces and E_k algebras - Kelly Wang\, University of Cambridg
 e 
DTSTART:20250228T160000Z
DTEND:20250228T170000Z
UID:TALK225631@talks.cam.ac.uk
CONTACT:Adrian Dawid
DESCRIPTION:Loop spaces (:= based homotopy classes of maps from the circle
 ) are fundamental objects in algebraic topology. They admit a binary opera
 tion that is “associative and to-some-level-commutative\, up to coherent
  higher homotopy”. The thing inside parenthesis can be made formally int
 o the statement that a k-fold loop space is a E_k algebra in spaces ( ~= s
 paces with an action of configuration of cubes in R^k). Under some conditi
 ons the converse is also true. \n\nThis talk will introduce basic definiti
 ons in the theory\, give a lot of examples\, and make the paragraph above 
 precise. If time permits\, we shall also see some E_k algebras not arising
  as loop spaces (e.g. some algebraic examples)\, and maybe homological fea
 tures of those.
LOCATION:MR13
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