Results 11 to 20 of about 48,683 (227)
Non-Compact Symplectic Toric Manifolds [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 A key result in equivariant symplectic geometry is Delzant's classification of compact connected symplectic toric manifolds. The moment map induces an embedding of the quotient of the manifold by the torus action into the dual of the Lie algebra of the ...
Karshon, Yael, Lerman, Eugene
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Symplectic Groupoids of Log Symplectic Manifolds [PDF]
International Mathematics Research Notices, 2013 A log symplectic manifold is a Poisson manifold which is generically nondegenerate. We develop two methods for constructing the symplectic groupoids of log symplectic manifolds. The first is a blow-up construction, corresponding to the notion of an elementary modification of a Lie algebroid along a subalgebroid.
Gualtieri, Marco, Li, Songhao
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Near-symplectic 2n–manifolds [PDF]
Algebraic & Geometric Topology, 2016 We give a generalization of the concept of near-symplectic structures to 2n dimensions. According to our definition, a closed 2-form on a 2n-manifold M is near-symplectic, if it is symplectic outside a submanifold Z of codimension 3, where ^{n-1} vanishes. This extends the concept known in dimension 4.
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Lagrangian submanifolds and Lefschetz pencils [PDF]
, 2004 Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold.
Auroux, Denis +2 more
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SYMPLECTIC SURFACES IN SYMPLECTIC 4-MANIFOLDS
Taiwanese Journal of Mathematics, 2003 Let \(X\) be a closed, minimal, symplectic 4-manifold with symplectic form \(\omega,\) and \(F\) a symplectic surface in \(X\) satisfying \(c_1(TX)[F] > 0.\) D. McDuff asked whether it follows that \(X\) must be rational or ruled. Partial results have been obtained by \textit{D. McDuff} in [J. Am. Math. Soc. 3, 679-712 (1990; Zbl 0723.53019); J.
Cho, Mi Sung, Cho, Yong Seung
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Symplectic torus actions with coisotropic principal orbits [PDF]
, 2006 In this paper we completely classify symplectic actions of a torus $T$ on a compact connected symplectic manifold $(M, \sigma)$ when some, hence every, principal orbit is a coisotropic submanifold of $(M, \sigma)$. That is, we construct an explicit model,
Duistermaat, J. J., Pelayo, A.
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Calculus on symplectic manifolds [PDF]
Archivum Mathematicum, 2018 On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic form, we find a new complex.
Eastwood, Michael, Slovák, Jan
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Floer-Novikov cohomology and symplectic fixed points, revisited
Pracì Mìžnarodnogo Geometričnogo Centru, 2020 This note is mostly an exposition of a few versions of Floer-Novikov cohomology with a few new observations. For example, we state a lower bound for the number of symplectic fixed points of a non-degenerate symplectomorphism, which is symplectomorphic ...
Kaoru Ono, Hong Van Le
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Rabinowitz Floer homology and symplectic homology [PDF]
, 2009 The Rabinowitz-Floer homology groups $RFH_*(M,W)$ are associated to an exact embedding of a contact manifold $(M,\xi)$ into a symplectic manifold $(W,\omega)$. They depend only on the bounded component $V$ of $W\setminus M$.
Cieliebak, Kai +2 more
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SPECIAL SYMPLECTIC SIX-MANIFOLDS [PDF]
The Quarterly Journal of Mathematics, 2007 18 ...
CONTI D, TOMASSINI A
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