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X-WR-CALNAME:Vladimir Chernov: \"Legendrian links\, causality\, and the 
 Low conjecture\"
PRODID:-//Apple Computer\, Inc//iCal 2.0//EN
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METHOD:PUBLISH
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TZID:America/New_York
LAST-MODIFIED:20090205T201238Z
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DTSTART:20090308T070000
TZOFFSETTO:-0400
TZOFFSETFROM:+0000
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DURATION:PT1H
LOCATION:Math 520\, Columbia University
DTSTAMP:20090205T201232Z
UID:BBC9BE76-E7AA-49D3-99D2-A3424AE13D75
SEQUENCE:5
URL;VALUE=URI:http://math.columbia.edu/~lipshitz/SGGT/
DTSTART;TZID=America/New_York:20090424T124500
SUMMARY:Vladimir Chernov: \"Legendrian links\, causality\, and the Low c
 onjecture\"
DESCRIPTION:Let (X^{m+1}\, g) be a globally hyperbolic spacetime with Ca
 uchy surface diffeomorphic to an open subset of R^m. The Legendrian Low 
 conjecture formulated by Nat\\'ario and Tod says that two events x\,y\\i
 n X are causally related if and only if the Legendrian link of spheres S
 _x\, S_y whose points are light geodesics passing through x and y is non
 -trivial in the contact manifold of all light geodesics in X. The Low co
 njecture says that for m=2 the events x\,y are causally related if and o
 nly if S_x\, S_y is non-trivial as a topological link. We prove the Low 
 and the Legendrian Low conjectures. We also show that similar statements
  hold for any globally hyperbolic (X\, g) such that the universal cover 
 of its Cauchy surface is diffeomorphic to an open domain of R^m. An inte
 resting fact\, proved in the joint work with Yuli Rudyak\, is that a cer
 tain weakened version of the Low conjecture is true for all nonrefocussi
 ng globally hyperbolic spacetimes. This includes all the cases where a C
 auchy surface has infinite fundamental group or is not a closed manifold
 . (This is based on the joint work with Stefan Nemirovski.)
ORGANIZER;CN="Robert Lipshitz":mailto:lipshitz@math.stanford.edu
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