4 papers
math.SG2023
The complete classification of isotopy classes of degree three symplectic curves in via a novel algebraic theory of braid monodromy
Amitesh Datta
We develop a new algebraic theory of positive braids and conjugacy classes in the braid group . We use our theory to establish a complete classification of isotopy classes of…
math.RT2022
A strong characterization of the entries of the Burau matrices of -braids: The Burau representation of the braid group is faithful almost everywhere
Amitesh Datta
We establish strong constraints on the kernel of the (reduced) Burau representation of the braid group .…
math.NT2022
A novel connection between integral binary quadratic forms and knot polynomials
Amitesh Datta
We establish a novel connection between algebraic number theory and knot theory. We show that the number of equivalence classes of integral binary quadratic forms of discriminant $…
math.GT2020
The braid group in the framework of continued fractions
Amitesh Datta
We use the classical interpretation of the braid group as a central extension of the modular group to establish new and fundamental prop…