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The Dehn twist coefficient for big and small mapping class groups
Peter Feller, Diana Hubbard, Hannah Turner
We study a quasimorphism, which we call the Dehn twist coefficient (DTC), from the mapping class group of a surface (with a chosen compact boundary component) that generalizes the…
Examples of non-minimal open books with high fractional Dehn twist coefficient
Peter Feller, Diana Hubbard
In this short note we construct examples of open books for 3-manifolds that show that arbitrarily high twisting of the monodromy of the open book does not guarantee maximality of t…
Braids, fibered knots, and concordance questions
Diana Hubbard, Keiko Kawamuro, Feride Ceren Kose +5
Given a knot in , one can associate to it a surface diffeomorphism in two different ways. First, an arbitrary knot in can be represented by braids, which can be though…
On the Upsilon invariant of fibered knots and right-veering open books
Dongtai He, Diana Hubbard, Linh Truong
We give a sufficient condition using the Ozsváth-Stipsicz-Szabó concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering…
Stability and triviality of the transverse invariant from Khovanov homology
Diana Hubbard, Christine Ruey Shan Lee
We explore properties of braids such as their fractional Dehn twist coefficients, right-veeringness, and quasipositivity, in relation to the transverse invariant from Khovanov homo…
On Sutured Khovanov Homology and Axis-Preserving Mutations
Diana Hubbard
This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship betwee…