Siddhartha Gadgil
Articles written in Proceedings – Mathematical Sciences
Volume 114 Issue 2 May 2004 pp 153-158
Limits of functions and elliptic operators
We show that a subspace
Volume 115 Issue 3 August 2005 pp 251-257
Homeomorphisms and the homology of non-orientable surfaces
Siddhartha Gadgil Dishant Pancholi
We show that, for a closed non-orientable surface
Volume 120 Issue 2 April 2010 pp 217-241
Splittings of Free Groups, Normal Forms and Partitions of Ends
Siddhartha Gadgil Suhas Pandit
Splittings of a free group correspond to embedded spheres in the 3-manifold $M=\sharp_k S^2\times S^1$. These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of
Volume 126 Issue 2 May 2016 pp 261-275 Research Article
Relative symplectic caps, 4-genus and fibered knots
SIDDHARTHA GADGIL DHEERAJ KULKARNI
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 $\Sigma$ in $X$ such that $\delta\Sigma$ is a transverse knot in $\delta X$. In this paper, we prove that there is a closed symplectic 4-manifold $Y$ with a closed symplectic surface $S$ such that $(X, \Sigma)$ 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 $\mathbb S^3$. Further, we give a criterion for quasipositive fibered knots to be strongly quasipositive.
Volume 130, 2020
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