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.
|
PDF
Pro_Ind_Aca_Sci_126-2_261_2016.pdf - Published Version Download (440kB) | Preview |
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 |
|---|---|
| Publication: | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES |
| Publisher: | INDIAN ACAD SCIENCES |
| 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 |
| Date Deposited: | 16 Jun 2016 05:01 |
| Last Modified: | 16 Jun 2016 05:01 |
| URI: | http://eprints.iisc.ac.in/id/eprint/53970 |
Actions (login required)
 |
View Item |
