Orbifold adjunction formula and symplectic cobordisms between lens spaces

Chen, Weimin

doi:10.2140/gt.2004.8.701

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Orbifold adjunction formula and symplectic cobordisms between lens spaces

Weimin Chen

Geometry & Topology 8 (2004) 701–734

DOI: 10.2140/gt.2004.8.701

arXiv: math.GT/0403395

Abstract

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.

Keywords

cobordism of lens spaces, orbifold adjunction formula, symplectic 4–orbifolds, pseudoholomorphic curves

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 57R80

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Publication

Received: 27 December 2003

Revised: 20 January 2004

Accepted: 3 May 2004

Published: 16 May 2004

Proposed: Yasha Eliashberg

Seconded: Robion Kirby, Ronald Fintushel

Authors

Weimin Chen
Mathematics Department Tulane University New Orleans Louisiana 70118 USA

Volume 8, issue 2 (2004)