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Lagrangian topology and
enumerative geometry
Paul Biran and Octav Cornea |
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Geometry & Topology 16 (2012) 963–1052
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Abstract |
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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 –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. |
Keywords
Lagrangian submanifold, quantum homology, Floer homology,
quadratic form, toric manifold
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Mathematical Subject Classification 2010
Primary: 53D12, 53D40
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References |
Publication
Received: 14 June 2011
Revised: 3 February 2012
Accepted: 4 March 2012
Published: 22 May 2012
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Simon Donaldson
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Authors |
| Paul Biran | |
| Department of Mathematics ETH-Zürich Rämistrasse 101 CH-8092 Zürich Switzerland |
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| Octav Cornea | |
| Department of Mathematics and
Statistics University of Montreal CP 6128 succ. Centre-ville Montréal QC H3C 3J7 Canada |
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| http://www.dms.umontreal.ca/~cornea/ | |
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