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X-WR-CALNAME:Soren Galatius: \"Holomorphic curves and stable homotopy th
 eory.\"
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LAST-MODIFIED:20071127T194910Z
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DURATION:PT1H
LOCATION:Math 312\, Columbia University
DTSTAMP:20071127T194852Z
UID:92C5DF03-FCD2-4C97-933D-A084C4BFFC77
SEQUENCE:8
URL;VALUE=URI:http://math.columbia.edu/~lipshitz/SGGT/
DTSTART;TZID=US/Eastern:20071207T171500
SUMMARY:Soren Galatius: \"Holomorphic curves and stable homotopy theory.
 \"
DESCRIPTION:Abstract: Let M(X) denote the moduli space of (nodal\, stabl
 e\, genus g) curves holomorphic curves in X.  Invariants (e.g. Gromov-Wi
 tten) can be extracted from two ingredients: (Parts of) the cohomology r
 ing H^*(M(X))\, and the fundamental class H^*(M(X)) -> Q.  I will descri
 be a space F(X) and a natural map u: M(X) -> F(X).  From the point of vi
 ew of stable homotopy theory\, the definition of the space F(X) is a rat
 her natural construction\, and in particular the rational cohomology rin
 g of F(X) can be easily and explicitly described.  All relevant cohomolo
 gy classes in M(X) arise as pull back from classes in F(X). This framewo
 rk collects all the \"homotopy theoretic\" information into one object\,
  and all the \"analytic\" information is encoded in the fundamental clas
 s H^*(F(X)) -> Q.  In the case where X is a point (my talk will focus on
  this case)\, the fundamental class \"is\" the power\nseries determined 
 by Kontsevich's theorem (Witten's conjecture).  This is joint work with 
 Ya. Eliashberg.
ORGANIZER;CN="Robert Lipshitz":mailto:lipshitz@math.stanford.edu
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