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Dishant M. Pancholi

Publications and source records attributed to Dishant M. Pancholi.

8 recordsLinked to original sources
arXiv2021

Symplectic embeddings of 4-manifolds via Lefschetz fibrations

In this article we study proper symplectic and iso-symplectic embeddings of $4$--manifolds in $6$--manifolds. We show that a closed orientable smooth $4$--manifold admitting a Lefschetz fibration over $\C P^1$ admits a symplectic embedding in the symplectic manifold $(\C P^1 \times \C P^1 \times \C P^1, ω_{pr}),$ where $ω_{pr}$ is the product symplectic form on $\C P^1 \times \C P^1 \times \C P^1.$ We also show that there exists a sub-critical Weinstein $6$--manifold in which all finite type Weinstein $4$--manifolds admit iso-symplectic embeddings.

math.GT↗
arXiv2019

Iso-contact embeddings of manifolds in co-dimension $2$

The purpose of this article is to study co-dimension $2$ iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold $(M^{2n-1}, ξ_M)$ iso-contact embeds in a contact manifold $(N^{2n+1}, ξ_N),$ provided $M$ contact embeds in $(N, ξ_N)$ with a trivial normal bundle and the contact structure induced on $M$ via this embedding is homotopic as an almost-contact structure to $ξ_M.$ We apply this result to first establish that a closed contact $3$--manifold having no $2$--torsion in its second integral cohomology iso-contact embeds in the standard contact $5$--sphere if and only if the first Chern class of the contact structure is zero. Finally, we discuss iso-contact embeddings of closed simply connected contact $5$--manifolds.

math.SG↗
arXiv2019

The Legendrian Whitney trick

In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to show the existence h-principle for codimension-two contact embeddings with a prescribed contact structure.

math.SG↗
arXiv2018

Embeddings of $3$--manifolds via open books

In this note, we discuss embeddings of $3$--manifolds via open books. First we show that every open book of every closed orientable $3$--manifold admits an open book embedding in any open book decompistion of $S^2 \times S^3$ and $S^2 \widetilde{\times} S^3$ with the page a disk bundle over $S^2$ and monodromy the identity. We then use open book embeddings to reprove that every closed orientable $3$--manifold embeds in $S^5.$

math.GT↗
arXiv2015

On generalizing Lutz twists

We give a possible generalization of Lutz twist to all dimensions. This reproves the fact that every contact manifold can be given a non-fillable contact structure and also shows great flexibility in the manifolds that can be realized as cores of overtwisted families. We moreover show that $R^{2n+1}$ has at least three distinct contact structures. This version of the paper contains both the texts of the published version of the paper together with an Erratum to the published version appended to the end.

math.SG↗
arXiv2013

Contact Blow-Up

We provide various definitions for the contact blow--up. Such different approaches to the contact blow--up are related. Some uniqueness and non--uniqueness results are also provided.

math.SG↗