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2007•Journal of Symplectic GeometryOpen access

Symplectic hypersurfaces and transversality in Gromov-Witten theory

Kai Cieliebak, Klaus Mohnke

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Abstract

We present a new method to prove transversality for holomorphic curves in symplectic manifolds, and show how it leads to a definition of genus zero Gromov-Witten invariants.The main idea is to introduce additional marked points that are mapped to a symplectic hypersurface of high degree in order to stabilize the domains of holomorphic maps.

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We present a new method to prove transversality for holomorphic curves in symplectic manifolds, and show how it leads to a definition of genus zero Gromov-Witten invariants.The main idea is to introduce additional marked points that are mapped to a symplectic hypersurface of high degree in order to stabilize the domains of holomorphic maps.

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Available abstract

We present a new method to prove transversality for holomorphic curves in symplectic manifolds, and show how it leads to a definition of genus zero Gromov-Witten invariants.The main idea is to introduce additional marked points that are mapped to a symplectic hypersurface of high degree in order to stabilize the domains of holomorphic maps.

Key concepts: Transversality, Hypersurface, Mathematics, Symplectic geometry, Holomorphic function, Pure mathematics, Genus, Symplectomorphism

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