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X-WR-CALNAME:Daniel Mathews: \"Chord diagrams\, topological quantum fiel
 d theory\, and the sutured Floer homology of solid tori\"
PRODID:-//Apple Computer\, Inc//iCal 2.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
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TZID:America/New_York
LAST-MODIFIED:20090405T002339Z
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DTSTART:20090308T070000
TZOFFSETTO:-0400
TZOFFSETFROM:+0000
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DURATION:PT1H
LOCATION:Math 520\, Columbia University
DTSTAMP:20090405T002332Z
UID:1C9D3A19-BE9A-40DF-A253-13038E9088B0
SEQUENCE:6
URL;VALUE=URI:http://math.columbia.edu/~lipshitz/SGGT/
DTSTART;TZID=America/New_York:20090417T154500
SUMMARY:Daniel Mathews: \"Chord diagrams\, topological quantum field the
 ory\, and the sutured Floer homology of solid tori\"
DESCRIPTION:Abstract:  I will talk about recent investigations of contac
 t elements in the sutured Floer homology of solid tori\, as part of the 
 (1+1)-dimensional TQFT defined by Honda-Kazez-Matic. The Z_2 sutured Flo
 er homology vector spaces in this case form a \"categorification of Pasc
 al's\ntriangle\"\, a triangle of vector spaces\, with contact elements\n
 corresponding to chord diagrams and forming distinguished subsets of ord
 er given by the Narayana numbers. Sutured Floer homology in this case re
 duces to the combinatorics of chord diagrams --- so that this talk is ac
 tually very elementary.\n\nI will show that there are natural \"creation
  and annihilation operators\" which allow us to define a QFT-type basis 
 consisting of\ncontact elements\; and contact elements are in bijective 
 correspondence with comparable pairs of basis elements with respect to a
  certain partial order\, and in a natural and explicit way. I will expla
 in how we can use this to extend Honda's notion of contact category to a
  2-category\, and possibly a 3-category.
ORGANIZER;CN="Robert Lipshitz":mailto:lipshitz@math.stanford.edu
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