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Tangles and persistent dynamical invariants
by
Dan Silver
Univ. of South Alabama and UMD
A tangle t embeds in a link l if some diagram of t extends to a diagram of l. In his Ph.D. thesis D. Krebes proved that if t is a 4-tangle embedded in l such that both the numerator and denominator closures admit nontrivial Fox n-colorings, then l also admits a nontrivial n-coloring. His result was later generalized by D. Silver and S. Williams and also by D. Ruberman. A dynamical system can be associated to a link in a variety of ways. In one such dynamical system Fox n-colorings appear as period-2 points. We discuss symbolic dynamical systems associated to a tangle t that persist in l whenever the tangle embeds. We show that F. Ladrappier's "3-dot example" arises in this way.
Date received: November 29, 2000
Copyright © 2000 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cafy-05.