Lagrangian submanifolds and moment convexity
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- by Bernhard Krötz and Michael Otto PDF
- Trans. Amer. Math. Soc. 358 (2006), 799-818 Request permission
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.References
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Additional Information
- Bernhard Krötz
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1221
- Email: kroetz@math.uoregon.edu
- Michael Otto
- Affiliation: Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio
- Email: otto@math.ohio-state.edu
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 799-818
- MSC (2000): Primary 53D20, 22E15
- DOI: https://doi.org/10.1090/S0002-9947-05-03723-2
- MathSciNet review: 2177041