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Invariants for Lagrangian
tori
Ronald Fintushel and Ronald J Stern |
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Geometry & Topology 8 (2004) 947–968
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arXiv: math.SG/0304402 |
Abstract |
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We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4–manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We further show that for a large class of examples that is actually a invariant. In addition, this invariant is used to show that many symplectic 4–manifolds have nontrivial homology classes which are represented by infinitely many pairwise inequivalent Lagrangian tori, a result first proved by S Vidussi for the homotopy K3–surface obtained from knot surgery using the trefoil knot. |
Keywords
$4$–manifold, Seiberg–Witten invariant, symplectic,
Lagrangian
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Mathematical Subject Classification 2000
Primary: 57R57
Secondary: 57R17
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References |
Forward citations |
Publication
Received: 4 September 2003
Revised: 19 April 2004
Accepted: 3 June 2004
Published: 29 June 2004
Proposed: Peter Kronheimer
Seconded: Robion Kirby, Yasha Eliashberg
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Authors |
| Ronald Fintushel | |
| Department of Mathematics Michigan State University East Lansing Michigan 48824 USA |
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| Ronald J Stern | |
| Department of Mathematics University of California Irvine California 92697 USA |
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