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VERSION:2.0
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SUMMARY:Manifold calculus beyond space-valued functors
DTSTART:20260206T101500
DTEND:20260206T111500
DTSTAMP:20260314T205938Z
UID:ab8e3d38fe2c821914d385c641d3b917d210dbddf56fcc2b97d48afb
CATEGORIES:Conferences - Seminars
DESCRIPTION:Kensuke Arakawa\, Kyoto University\nManifold calculus is a ho
 motopy-theoretic technique to study presheaves on manifolds\, which decomp
 oses them into successive approximations called polynomial approximations.
  First invented by Weiss to study embedding spaces\, it has become an impo
 rtant toolset for homotopical study of manifolds. \n\nLike ordinary calcu
 lus\, manifold calculus has two "fundamental theorems\," one which classif
 ies polynomial presheaves\, and the other that classifies homogeneous pres
 heaves. Consistent with his goal to study embedding spaces\, Weiss establi
 shed these theorems for space-valued presheaves. \n\nFrom the perspective
  of studying manifold invariants\, it is extremely natural to develop mani
 fold calculus for presheaves with more general values\, such as spectra an
 d chain complexes. However\, Weiss's proof of the fundamental theorems rel
 ies on ad-hoc constructions on spaces\, which do not seem to generalize ea
 sily. \n\nIn this talk\, I will explain that the two fundamental theorems
  do not depend on space-level constructions. Consequently\, they extend to
  presheaves valued in essentially any infinity category. This talk is base
 d on my paper "A context for manifold calculus" (arXiv:2403.03321).\n 
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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