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Stephen Humphries

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320 TMCB
Brigham Young University
Provo, UT 84602


+1 801 422 3370


+1 801 422 0504

Here is my CV

Here are some of my most recent papers:


Here is the representations of braid groups paper in dvi format. In this paper I construct representations of B3, B4 and B5 using the action of the braid groups on curves on an n-punctured disc. I get representations of degrees 4, 11 and 39 respectively. Some linear representations of braid groups.

To access maple file for the paper "Some Linear Representations of Braid Groups" click here. This file contains the matrices for the 11x11 and 39x39 matrices for the above representations together with matrices representing fixed forms for the corresponding representations.

Here is the Lie groups paper in dvi format Braid groups, infinite Lie algebras of Cartan type and rings of invariants. In this paper I represent pure braids as exponentiated derivations in an infinite-dimensional Lie algebra. This is related to the Magnus expansion of the free group. This has appeared in Topology and its Applications vol.  95 (1999) pages 173-205.

Here is the Hodge algebra paper in dvi format. In this paper I show that the braid groups B3, B4 act on an algebra with straightening law (ASL) where the partial order for B4 is based on a triangulation of the 2-sphere. I also calculate the Poincare series for these rings which are trace rings and subrings of a polynomial ring. This has already appeared in Communications in Algebra. (volume 26 (1998)) Action of some Braid groups on Hodge algebras.

Here is the paper in which I show that B3, B4, B5 and B6 all have non-trivial torsion-free non-abelian quotients. For the paper in dvi format "Some torsion-free quotients of braid groups. This has appeared in the Journal of knot theory and its Ramifications (2000) pages 341-366.

The dvi files for the  paper  `Action of braid groups on determinantal ideals,
compact spaces and a stratification of Teichmuller space',  is "Action of braid groups on determinantal ideals, compact spaces and a stratification of Teichmuller space" . For pdf file: pdf.

Here is a paper  called "Representations of Braid groups via determinantal rings" where I construct representations of braid groups over the ring of rational functions C(u) over a commutative ring with identity C using an action of braid groups on a determinantal variety, paralleling the classical case of GL(n). These representations fix a non-degenerate form which is unitary with respect to a certain involution. dvi  or pdf.


Here is the weak Cayley table paper in dvi format Weak Cayley table Functions. In this paper I study bijections f:G -> G such that f(gg') is conjugate to f(g)f(g') for all g,g' in G and which act on conjugacy classes. This appeared in Journal of Algebra vol 216 in 1999 pages 135-158.


Here are the two papers on Intersection number functions for curves on discs in dvi form "Intersection operators for curves on discs and Chebyshev polynomialsI or pdf . This has appeared in the Birmanfest.

and "Intersection operators for curves on discs II for dvi or pdf for pdf. This has appeared in Geometriae Dedicata.


Here is my paper describing chaotic behaviour of braid groups on certain compact topological spaces: dvi. The title is "Action of braid groups on compact spaces with chaotic behaviour". (35 pages, preprint 2001).

Here I describe the Hurwitz action on sequences of reflections generating finite reflection groups: frg.dvi,


A complete list of my publications: pdf.