4 papers
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…