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

Prelegent(ci)

Anzor Beridze

Afiliacja

Batumi State University

Język referatu

angielski

Termin

4 listopada 2026 10:30

Pokój

p. 4070

Seminarium

Seminarium „Topologia algebraiczna”

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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.

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