Papers by Dheeraj Dattatray Kulkarni
arXiv (Cornell University), Aug 12, 2016
In this paper, we explore minimal contact triangulations on contact 3-manifolds. We give many exp... more In this paper, we explore minimal contact triangulations on contact 3-manifolds. We give many explicit examples of contact triangulations that are close to minimal ones. The main results of this article say that on any closed oriented 3-manifold the number of vertices for minimal contact triangulations for overtwisted contact structures grows at most linearly with respect to the relative d 3 invariant. We conjecture that this bound is optimal. We also discuss contact triangulations for a certain family of overtwisted contact structures on 3-torus.
Topology and its Applications, 2016
In this note, we exhibit infinite families of tight non-fillable contact manifolds supported by p... more In this note, we exhibit infinite families of tight non-fillable contact manifolds supported by planar open books with vanishing Heegaard Floer contact invariants. Moreover, we also exhibit an infinite such family where the supported manifold is hyperbolic.
Proceedings - Mathematical Sciences, 2016
We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterio... more 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 Σ in X such that ∂Σ is a transverse knot in ∂X. In this paper, we prove that there is a closed symplectic 4-manifold Y with a closed symplectic surface S such that (X, Σ) 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 S 3. Further, we give a criterion for quasipostive fibered knots to be strongly quasipositive.
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Papers by Dheeraj Dattatray Kulkarni