Lagrangian topology and enumerative geometry

被引:33
|
作者
Biran, Paul [1 ]
Cornea, Octav
机构
[1] ETH, Dept Math, CH-8092 Zurich, Switzerland
基金
加拿大自然科学与工程研究理事会;
关键词
QUANTUM COHOMOLOGY; FLOER COHOMOLOGY; TORUS FIBERS; RIGIDITY; RINGS;
D O I
10.2140/gt.2012.16.963
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We analyze the properties of Lagrangian quantum homology (in the form constructed in our previous work, based on the pearl complex) to associate certain enumerative invariants to monotone Lagrangian submanifolds. The most interesting such invariant is given as the discriminant of a certain quadratic form. For 2-dimensional Lagrangians it corresponds geometrically to counting certain types of configurations involving pseudoholomorphic disks that are associated to triangles on the respective surface. We analyze various properties of these invariants and compute them and the related structures for a wide class of toric fibers. An appendix contains an explicit description of the orientation conventions and verifications required to establish quantum homology and the related structures over the integers.
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页码:963 / 1052
页数:90
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