Orbifold adjunction formula and symplectic cobordisms between lens spaces

Details Orbifold adjunction formula and symplectic cobordisms between lens spaces Orbifold adjunction formula and symplectic cobordisms between lens spaces

2004-03-23

arxiv.org/abs/math/0403395v2

Geom. Topol. 8(2004) 701-734

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper18.abs.html

Scientific paper

Each lens space has a canonical contact structure which lifts to the distribution of complex lines on the three-sphere. In this paper, we show that a symplectic homology cobordism between two lens spaces, which is given with the canonical contact structure on the boundary, must be diffeomorphic to the product of a lens space with the unit interval. As one of the main ingredients in the proof, we also derive in this paper the adjunction and intersection formulae for pseudoholomorphic curves in an almost complex 4-orbifold, extending the relevant work of Gromov and McDuff in the manifold setting.

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