72 citations · 265 across the 34 of their papers we have counts for
36 papers
The Burau representation of the braid group is faithful for n = 4
Vasudha Bharathram, Joan S. Birman, Tara E. Brendle
In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group…
The work of Jones
Joan S. Birman
In this article the discovery of the Jones Polynomial will be discussed, emphasizing the way in which it illustrated the remarkable unity between distinct parts of Mathematics, eac…
Distance and intersection number in the curve graph of a surface
Joan S. Birman, Matthew J. Morse, Nancy C. Wrinkle
In this work, we study the cellular decomposition of induced by a filling pair of curves and , , and its connection to the distance functi…
Efficient geodesics and an effective algorithm for distance in the complex of curves
Joan Birman, Dan Margalit, William Menasco
We give an algorithm for determining the distance between two vertices of the complex of curves. While there already exist such algorithms, for example by Leasure, Shackleton, and…
Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface
Joan Birman, Nathan Broaddus, William Menasco
Aramayona and Leininger have provided a "finite rigid subset" of the curve complex of a surface , characterized by the fact that any si…
The curve complex has dead ends
Joan S. Birman, William W. Menasco
It is proved that the curve graph of a surface has a local pathology that had not been identified as such: there are vertices in such that is…