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2013•arXiv (Cornell University)Open access

SYMPLECTIC TOPOLOGY OF b-SYMPLECTIC MANIFOLDS

Pedro Frejlich, David Mart, Inêz Ohashi Torres, Eva Miranda

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Abstract

A Poisson manifold \\((M^{2n}, \\pi)\\) is \\(b\\)-symplectic if \\(\\bigwedge^{n}\\pi\\) is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to \\(b\\)-symplectic manifolds. The main results provide constructions of: \\(b\\)-symplectic submanifolds à la Donaldson, \\(b\\)-symplectic structures on open manifolds by Gromov’s \\(h\\)-principle, and of \\(b\\)-symplectic manifolds with a prescribed singular locus, by means of surgeries.

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What this paper is about

A Poisson manifold \\((M^{2n}, \\pi)\\) is \\(b\\)-symplectic if \\(\\bigwedge^{n}\\pi\\) is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to \\(b\\)-symplectic manifolds. The main results provide constructions of: \\(b\\)-symplectic submanifolds à la Donaldson, \\(b\\)-symplectic structures on open manifolds by Gromov’s \\(h\\)-principle, and of \\(b\\)-symplectic manifolds with a prescribed singular locus, by means of surgeries.

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Available abstract

A Poisson manifold \\((M^{2n}, \\pi)\\) is \\(b\\)-symplectic if \\(\\bigwedge^{n}\\pi\\) is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to \\(b\\)-symplectic manifolds. The main results provide constructions of: \\(b\\)-symplectic submanifolds à la Donaldson, \\(b\\)-symplectic structures on open manifolds by Gromov’s \\(h\\)-principle, and of \\(b\\)-symplectic manifolds with a prescribed singular locus, by means of surgeries.

Key concepts: Symplectic geometry, Symplectic manifold, Symplectomorphism, Moment map, Symplectic vector space, Symplectic representation, Symplectic matrix, Pure mathematics

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