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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Lagrangian submanifolds and moment convexity

Authors: Bernhard Krötz and Michael Otto
Journal: Trans. Amer. Math. Soc. 358 (2006), 799-818
MSC (2000): Primary 53D20, 22E15
Published electronically: May 10, 2005
MathSciNet review: 2177041
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Abstract: We consider a Hamiltonian torus action $T\times M \rightarrow M$ on a compact connected symplectic manifold $M$ and its associated momentum map $\Phi $. For certain Lagrangian submanifolds $Q\subseteq M$ we show that $\Phi (Q)$ is convex. The submanifolds $Q$ arise as the fixed point set of an involutive diffeomorphism $\tau :M\rightarrow M$ which satisfies several compatibility conditions with the torus action, but which is in general not anti-symplectic. As an application we complete a symplectic proof of Kostant's non-linear convexity theorem.

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Additional Information

Bernhard Krötz
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1221

Michael Otto
Affiliation: Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio

PII: S 0002-9947(05)03723-2
Received by editor(s): November 11, 2003
Received by editor(s) in revised form: March 31, 2004
Published electronically: May 10, 2005
Additional Notes: The work of the first author was supported in part by NSF grant DMS-0097314
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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