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A note on the symplectic topology of b-manifolds

Miranda Galcerán, Eva, David Martínez Torres, Pedro Frejlich

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Abstract

Poisson manifold (M2n; ) is b-symplectic if\nVn is transverse\nto the zero section. In this paper we apply techniques native to Symplectic\nTopology to address questions pertaining to b-symplectic manifolds. We pro-\nvide constructions of b-symplectic structures on open manifolds by Gromov's\nh-principle, and of b-symplectic manifolds with a prescribed singular locus, by\nmeans of surgeries.

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What this paper is about

Poisson manifold (M2n; ) is b-symplectic if\nVn is transverse\nto the zero section. In this paper we apply techniques native to Symplectic\nTopology to address questions pertaining to b-symplectic manifolds. We pro-\nvide constructions of b-symplectic structures on open manifolds by Gromov's\nh-principle, and of b-symplectic manifolds with a prescribed singular locus, by\nmeans of surgeries.

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Available abstract

Poisson manifold (M2n; ) is b-symplectic if\nVn is transverse\nto the zero section. In this paper we apply techniques native to Symplectic\nTopology to address questions pertaining to b-symplectic manifolds. We pro-\nvide constructions of b-symplectic structures on open manifolds by Gromov's\nh-principle, and of b-symplectic manifolds with a prescribed singular locus, by\nmeans of surgeries.

Key concepts: Symplectic geometry, Mathematics, Symplectic manifold, Symplectomorphism, Pure mathematics, Moment map, Manifold (fluid mechanics), Symplectic vector space

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