9 papers
Contact cosmetic surgery on Legendrian knots in integer homology sphere -spaces
Apratim Chakraborty, Swarup Kumar Das, Tanushree Shah
We extend the study of contact cosmetic surgeries to Legendrian knots in integer homology sphere L-spaces . We prove that the contact cosmetic surgery conjecture holds for all non-…
On Legendrian Thurston-Bennequin-symmetrical graphs
Trung Chau, Tanushree Shah
This article reviews the development of Legendrian graph theory in the standard contact 3-sphere (). We provide a generalized criterion under which the total Thurston…
A note on alternating knots in handlebodies
Lizzie Buchanan, Tanushree Shah
We establish a Kauffman-Murasugi-Thistlethwaite-type theorem for alternating knots in a solid torus. Specifically, we show that any dotted-reduced alternating diagram of a knot in…
Mixed tori in contact surgery diagrams
Austin Christian, Tanushree Shah
We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplec…
Non-Simple knots in Contact 3-Manifolds
Ipsita Datta, Tanushree Shah
We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is ric…
Tight contact structures on toroidal plumbed 3-manifolds
Tanushree Shah, Jonathan Simone
We consider tight contact structures on plumbed 3-manifolds with no bad vertices. We discuss how one can count the number of tight contact structures with zero Giroux torsion on su…
On contact cosmetic surgery
John B. Etnyre, Tanushree Shah
We demonstrate that the contact cosmetic surgery conjecture holds true for all non-trivial Legendrian knots, with the possible exception of Lagrangian slice knots. We also discuss…
On The Cost Function Associated With Legendrian Knots
Dheeraj Kulkarni, Tanushree Shah, Monika Yadav
In this article, we introduce a non-negative integer-valued function that measures the obstruction for converting topological isotopy between two Legendrian knots into a Legendrian…
Classification of tight contact structures on some Seifert fibered manifolds: I
Tanushree Shah
We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structu…