Burau representation for n = 4: The problem of faithfulness - algebraic vs topological approach

Speaker(s)

Anzor Beridze

Affiliation

Batumi State University

Language of the talk

English

Date

Nov. 4, 2026, 10:30 a.m.

Room

room 4070

Seminar

Seminar Algebraic Topology

---

The problem of the faithfulness of the Burau representation for n = 4 appears to have been solved affirmatively by Joan Birman and her coauthors.
We briefly describe the topological approach that led to this remarkable result, using some elementary homotopy theory.
We also describe our own attempts to solve the same problem by treating it as a purely linear algebraic question. This reduces to asking whether certain matrices A and B, whose entries are Laurent polynomials, generate a free group of rank two. This is, in turn, a classical problem in mathematics, and we hope that it admits a solution based solely on linear algebra, independent of any topological considerations.

---