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Relative symplectic caps, 4-genus and fibered knots

Gadgil, Siddhartha and Kulkarni, Dheeraj (2016) Relative symplectic caps, 4-genus and fibered knots. In: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 126 (2). pp. 261-275.

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Official URL: http://dx.doi.org/10.1007/s12044-016-0278-3

Abstract

We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots. More precisely, suppose we have a symplectic 4-manifold X with convex boundary and a symplectic surface I pound in X such that a,I pound is a transverse knot in a, X. In this paper, we prove that there is a closed symplectic 4-manifold Y with a closed symplectic surface S such that (X,I ) pound embeds into (Y,S) symplectically. As a consequence we obtain a relative version of the symplectic Thom conjecture. We also prove a relative version of the sufficiency part of Giroux's criterion for Stein fillability, namely, we show that a fibered knot whose mondoromy is a product of positive Dehn twists bounds a symplectic surface in a Stein filling. We use this to study 4-genus of fibered knots in . Further, we give a criterion for quasipositive fibered knots to be strongly quasipositive.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the INDIAN ACAD SCIENCES, C V RAMAN AVENUE, SADASHIVANAGAR, P B #8005, BANGALORE 560 080, INDIA
Keywords: Relative symplectic caps; 4-genus and fibered knots
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 16 Jun 2016 05:01
Last Modified: 16 Jun 2016 05:01
URI: http://eprints.iisc.ac.in/id/eprint/53970

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