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SUMMARY:Geometric models for twisted K-homology - Thomas Schick (Georg-Aug
 ust-Universität Göttingen)
DTSTART:20170327T150000Z
DTEND:20170327T160000Z
UID:TALK71647@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>         Co-author: Paul Baum 		(Penn State University) 
        <br></span><br>K-homology\, the homology theory dual to K-theory\, 
 can be described in a  number of quite distinct models.  One of them is an
 alytic\, uses Kasparov&#39\;s KK-theory\, and is the home of  index proble
 ms. Another one uses geometric cycles\, going back to Baum  and Douglas. A
  large part of index theory is concerned with the  isomorphism between the
  geoemtric and the analytic model\, and with Chern  character transformati
 ons to (co)homology. <br><br>In applications to string theory\, and for ce
 rtain index problems\,  twisted versions of K-theory and K-homology play a
 n essential role. <br>  <span>&nbsp\;<br>We will descirbe the general cont
 ext\, and then focus on two new models  for twisted K-homology and their a
 pplications and relations. These aere  again based on geometric cycles in 
 the spirit of Baum and Douglas.  We will include in particular precise dis
 cussions of the different ways  to define and work with twists (for us\, c
 lassified by elements of the  third integral cohomology group of the base 
 space in question).</span>
LOCATION:Seminar Room 1\, Newton Institute
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