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PRODID:-//Memento EPFL//
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SUMMARY:Hopf invariants\, rational homotopy theory\, and physical integral
 s.
DTSTART:20160202T101500
DTEND:20160202T113000
DTSTAMP:20260428T064341Z
UID:f7a4da17aa23f8c16e0b6f1e5b2013042cf6ff5ad31f33005aaabab4
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dev Sinha\nWe discuss a basic question in algebraic topology: 
 given two maps f\,g : X —> Y\, how can we tell whether or not they are h
 omotopic?  One condition is that f and g should pull back cohomology in t
 he same way.  But even when X is a sphere\, this is far from sufficient.
   In relatively recent work\, Ben Walter and I resolve this question when
  X is a sphere and Y is simply connected\, rationally (that is\, up to the
 n multiplying f and g by some non-zero integer).  We do so by giving expl
 icit integrals\, generalizing Whitehead’s integral formula for the Hopf 
 invariant\, which has been cited regularly in the physics literature.  Th
 ese integrals are a concrete manifestation of Koszul duality.   These in
 tegrals are also similar to integrals developed by Cattaneo and Mnev in th
 e context of Chern-Simons theory.  We speculate on the connection\, as we
 ll as potential connection with L_\\infty models for rational homotopy the
 ory.
LOCATION:MA110
STATUS:CONFIRMED
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