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SUMMARY:An SU(3) variant of instanton homology for webs - Peter Kronheimer
  (Harvard University)
DTSTART:20170817T090000Z
DTEND:20170817T100000Z
UID:TALK75861@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Let <i>K</i> be a trivalent graph embedded in 3-space (a
  web). In an earlier talk at this conference\, Tom Mrowka outlined how one
  may define an instanton homology <i>J</i>(<i>K</i>) using gauge theory wi
 th structure group <i>SO</i>(3). This invariant is a vector space over <b>
 Z</b>/2 and has a conjectured relationship to Tait colorings of <i>K</i> w
 hen <i>K</i> is planar. In this talk\, we will explore a variant of this c
 onstruction\, replacing <i>SO</i>(3) with <i>SU</i>(3). With this modified
  version\, the dimension of the instanton homology is indeed equal to the 
 number of Tait colorings when <i>K</i> is planar. (Without the assumption 
 of planarity\, the dimension is sometimes larger\, sometimes smaller.) The
 re is a further variant\, with rational coefficients\, whose dimension is 
 equal to the number of Tait colorings always.<br></span><br>Coauthors: Tom
  Mrowka (MIT)<br><br>
LOCATION:Seminar Room 1\, Newton Institute
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