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SUMMARY:The homotopy type of algebraic cobordism categories - Fabian Hebes
 treit (University of Bonn)
DTSTART:20181205T113000Z
DTEND:20181205T123000Z
UID:TALK115378@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors: Baptiste Calm&egrave\;s (Universit&eacute\; d&#39\
 ;Artois)\, Emanuele Dotto (RFWU Bonn)\, Yonatan Harpaz (Universit&eacute\;
  Paris 13)\, Markus Land (Universit&auml\;t Regensburg)\, Kristian Moi (KT
 H Stockholm)\, Denis Nardin (Universit&eacute\; Paris 13)\, Thomas Nikolau
 s (WWU M&uuml\;nster)\, Wolfgang Steimle (Universit&auml\;t Augsburg). Abs
 tract: I will introduce cobordism categories of Poincar&eacute\; chain com
 plexes\, or more generally of Poincar&eacute\; objects in any hermitian qu
 asi-category C. One interest in such algebraic cobordism categories arises
  as they receive refinements of Ranicki&#39\;s symmetric signature in the 
 form of functors from geometric cobordism categories &agrave\; la Galatius
 -Madsen-Tillmann-Weiss. I will focus\, however\, on a more algebraic direc
 tion. The cobordism category of C can be delooped by an iterated Q-constru
 ction\, that is compatible with B&ouml\;kstedt-Madsen&#39\;s delooping of 
 the geometric cobordism category. The resulting spectrum is a derived vers
 ion of Grothendieck-Witt theory and I will explain how its homotopy type c
 an be computed in terms of the K- and L-Theory of C.
LOCATION:Seminar Room 1\, Newton Institute
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