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SUMMARY:The signature as a map of cobordism categories
DTSTART:20260416T121500Z
DTEND:20260416T131500Z
DTSTAMP:20260426T113500Z
UID:indico-event-115@indico.zdv.uni-mainz.de
DESCRIPTION:Speakers: Dominik Kirstein\n\nThe signature is a classical inv
 ariant of manifolds\, which is a shadow of their intersection form. More r
 efined topological indices of manifolds can be constructed by remembering 
 the full intersection form.In this talk\, I will explain how the signature
  has an enhancement to a multiplicative map from geometric cobordism spect
 ra of manifolds to algebraic cobordism spectra of Hermitian forms (known a
 s Grothendieck-Witt or L-theory). This crucially depends on the constructi
 on of the signature on the level of cobordism categories. \nThis approach 
 generalises and unifies various existing constructions in the literature. 
 I will conclude by explaining some interesting applications to geometric t
 opology\, such as a simple proof of the Weiss-Williams index theorem on ch
 aracteristic classes of manifold bundles.Based on work in progress with An
 drea Bianchi\, Fabian Hebestreit\, Kaif Hilman\, Christian Kremer\, Markus
  Land\, Thomas Nikolaus and Wolfgang Steimle.\n\nhttps://indico.zdv.uni-ma
 inz.de/event/115/
LOCATION:05-432 (Hilbertraum)
URL:https://indico.zdv.uni-mainz.de/event/115/
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