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SUMMARY:Nir Gadish (MIT)
DTSTART:20210405T203000Z
DTEND:20210405T213000Z
DTSTAMP:20260423T004754Z
UID:MITTop/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/28/">
 Möbius inversion in hömotopy theory</a>\nby Nir Gadish (MIT) as part of 
 MIT topology seminar\n\n\nAbstract\nMöbius inversion is classically a pro
 cedure in number theory that inverts summation of functions over the divis
 ors of an integer. A similar construction is possible for every locally fi
 nite poset\, and is governed by a so called Möbius function encoding the 
 combinatorics. In 1936 Hall observed that the values of the Möbius functi
 on are Euler characteristics of intervals in the poset\, suggesting a homo
 topy theoretic context for the inversion. In this talk we will discuss a f
 unctorial 'space-level' realization of Möbius inversion for diagrams taki
 ng values in a pointed cocomplete infinity-category. The role of the Möbi
 us function will be played by hömotopy types whose reduced Euler characte
 ristics are the classical values\, and inversion will hold up to extension
 s (think inclusion-exclusion but with the alternating signs replaced by ev
 en/odd spheres).\n\nThis provides a uniform perspective to many constructi
 ons in topology and algebra. Notable examples that I hope to mention inclu
 de handle decompositions\, Koszul resolutions\, and filtrations of configu
 ration spaces.\n
LOCATION:https://researchseminars.org/talk/MITTop/28/
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