Topological Entropy and Burau Representation Boris Kolev
نویسنده
چکیده
Let f be an orientation-preserving homeomorphism of the disk D, P a finite invariant subset and [fP ] the isotopy class of f in D \ P . We give a non trivial lower bound of the topological entropy for maps in [fP ], using the spectral radius of some specializations in GL(n,C) of the Burau matrix associated with [fP ] and we discuss some examples.
منابع مشابه
Entropy and the Burau Representation
The topological entropy of a braid is the infimum of the entropies of all homeomor-phisms of the disc which have a finite invariant set represented by the braid. When the isotopy class represented by the braid is pseudo-Anosov or is reducible with a pseudo-Anosov component, this entropy is positive. Fried and Kolev proved that the entropy is bounded below by the logarithm of the spectral radius...
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