6 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…
A condition on the Khovanov homology of three families of positive links
Lizzie Buchanan
In previous work, we developed diagram-independent upper bounds on the maximum degree of the Jones polynomial of three families of positive links. These families are characterized…
A condition on the Jones polynomial for a family of positive links
Lizzie Buchanan
We provide a bound on the maximum degree of the Jones polynomial of any positive link with second Jones coefficient equal to . This builds on the result of our previous work…
On the notion of Khovanov A-adequacy
Lizzie Buchanan, Huizheng Guo, Gabriel Montoya-Vega +2
The concept of adequate links, introduced by Lickorish and Thistlethwaite as a generalization of alternating links, has recently gained interest among knot theorists in the context…
A pair of Jones polynomial positivity obstructions
Lizzie Buchanan
We provide a new bound on the maximum degree of the Jones polynomial of a positive link with second Jones coefficient equal to or . This builds upon the result of ou…
A new condition on the Jones polynomial of a fibered positive link
Lizzie Buchanan
We give a new upper bound on the maximum degree of the Jones polynomial of a fibered positive link. In particular, we prove that the maximum degree of the Jones polynomial of a fib…