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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The h-cobordism category and A-theory - George Rap
tis (Universität Regensburg)
DTSTART;TZID=Europe/London:20181203T143000
DTEND;TZID=Europe/London:20181203T153000
UID:TALK115246AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/115246
DESCRIPTION:A fundamental link between Waldhausen'\;s algeb
raic K-theory of spaces (A-theory) and manifold to
pology is given by an identification of A-theory i
n terms of stable homotopy and the stable smooth
h-cobordism space. This important result has had m
any applications in the study of diffeomorphisms o
f manifolds. In more recent years\, the theory of
cobordism categories has provided a different app
roach to the study of diffeomorphism groups with s
pectacular applications. In collaboration with W.
Steimle \, we revisit the classical Waldhausen K-
theory in light of these developments and investig
ate new connections and applications. In this talk
\, I will first discuss a cobordism-type model fo
r A-theory\, and then I will focus on the h-cobord
ism category\, the cobordism category of h-cobordi
sms between smooth manifolds with boundary\, and
its relationship to the classical h-cobordism spac
e of a compact smooth manifold. This is joint work
with W. Steimle.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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