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Numerical invariants of the exponential groups and locally free approximation of the braid groups
by
Anatoly M. Vershik
Steklov Mathematical Institute at St. Petersburg
The entropy of the random walk on the countable group of the exponential growth could be used for comparison of the systems of the generators of the group. Fundamental inequality between growth, entropy and length of the words (which is similar to inequality between topological and metric entropy) allows to define a "natural" set of generators. For locally free groups and braid groups with natural generators it becomes a strict inequality.
Date received: August 11, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacy-55.