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X-WR-CALNAME:Anar Akhmedov: \"Exotic 4-manifolds with small Euler charac
 teristics.\"
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DURATION:PT1H
LOCATION:507 Math\, Columbia University
DTSTAMP:20070921T032107Z
UID:212DCE8E-0347-47C7-B8A4-5BC6086B5BFE
SEQUENCE:5
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SUMMARY:Anar Akhmedov: \"Exotic 4-manifolds with small Euler characteris
 tics.\"
DESCRIPTION:Abstract: It is known that many simply connected\, smooth to
 pological 4-manifolds admit infinitely many smooth structures. The small
 er the Euler characteristic\, the harder it is to construct exotic smoot
 h structure.\n\nIn this talk we present new examples of symplectic 4-man
 ifolds with same integral cohomology as S^2 x S^2. We also discuss the g
 eneralization of these examples to #_{2n-1}(S^2 x S^2) for n > 1. As an 
 application of these symplectic building blocks\, we construct exotic sm
 ooth structure on small 4-manifolds such as CP^2#k(-CP^2) for k = 2\, 3\
 , 4\, 5 and 3CP^2#l(-CP^2) for l=4\, 5\, 6\, 7. We will also discuss an 
 interesting applications to the geography of minimal symplectic 4-manifo
 lds.\n\nMost of this is joint work with B. Doug Park.
ORGANIZER;CN="Robert Lipshitz":mailto:lipshitz@math.stanford.edu
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