Entropies of braids

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Pseudo-Anosov homeomorphisms are classified by their invariant train tracks. The decomposition of any train track map in elementary folding maps gives a normal form for each train track class. In the case of 4-braids there are three train tracks classes and we give an explicit automaton that generates a normal form for each class. This enables us, for instance, to exhibit the pseudo-Anosov 4-braid with the minimal growth rate. We also show that the growth rate of a pseudo-Anosov braid appears as a root of the Alexander polynomial of a link that shares a common sub-link with the closure of the braid. We finally give a criterion for the faithfulness of the Burau representation for 4-braids.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2002-06
Language
English
Article Type
Article
Keywords

TRAIN-TRACKS; TOPOLOGICAL-ENTROPY; DIFFEOMORPHISMS; DISK

Citation

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.11, no.4, pp.647 - 666

ISSN
0218-2165
URI
http://hdl.handle.net/10203/83526
Appears in Collection
MA-Journal Papers(저널논문)
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