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X-FROM-URL:https://eom.sdu.dk/events/ical/f5e008ff-da02-4608-8a46-a5b972fb
 db04
X-WR-CALNAME:QM Research Seminar: A sheaf theoretic approach to homology m
 anifolds and Poincaré and Atiyah duality
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TZID:Europe/Copenhagen
X-LIC-LOCATION:Europe/Copenhagen
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DTSTAMP:20260513T130431Z
DTSTART:20261028T030000
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DESCRIPTION:[b]Speaker: Marco Volpe[/b] (MPIM Bonn) [nl]\n[b]Abstract:[/b]
 [nl]\nPoincaré and Atiyah duality theorems are fundamental results in the
  study of the (co)homology of smooth manifolds. However\, due to their pu
 rely cohomological nature\, one may naturally wonder whether it is necess
 ary to impose geometric conditions on a topological space to ensure the v
 alidity of these theorems. In this presentation\, we will review and rein
 terpret both Poincaré and Atiyah duality theorems using the framework of 
 sheaves of infinity categories. We will employ the formalism of six opera
 tions to extend these duality theorems beyond the realm of manifolds. Eve
 n more\, we will provide a comprehensive characterization of the class of
  topological spaces that satisfy Poincaré and Atiyah duality. This class 
 essentially consists of what are known as integral homology manifolds. Th
 is is a joint work with Markus Land.\n[nl]
DTEND:20231009T140000Z
DTSTAMP:20260513T130431Z
DTSTART:20231009T130000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
SEQUENCE:0
SUMMARY:QM Research Seminar: A sheaf theoretic approach to homology manifo
 lds and Poincaré and Atiyah duality
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