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Mat. Zametki, 2011, Volume 89, Issue 4, Pages 577–588 (Mi mz8293)  

This article is cited in 4 scientific papers (total in 4 papers)

Small Braids with Large Ultra Summit Set

M. Prasolov

M. V. Lomonosov Moscow State University

Abstract: In [1; Open question 2], the following question was posed: Is the size of the ultra summit set of the conjugacy class of a rigid pseudo-Anosov braid bounded above by a polynomial in the braid length and the number of strands? A negative answer to this question is given.

Keywords: braid group, conjugacy problem, ultra summit set, rigid pseudo-Anosov braid, left normal form, Garside element, Birman–Ko–Lee presentation

DOI: https://doi.org/10.4213/mzm8293

Full text: PDF file (448 kB)
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English version:
Mathematical Notes, 2011, 89:4, 545–554

Bibliographic databases:

UDC: 512.54
Received: 14.03.2009

Citation: M. Prasolov, “Small Braids with Large Ultra Summit Set”, Mat. Zametki, 89:4 (2011), 577–588; Math. Notes, 89:4 (2011), 545–554

Citation in format AMSBIB
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\paper Small Braids with Large Ultra Summit Set
\jour Mat. Zametki
\yr 2011
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\pages 577--588
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Calvez M., “Dual Garside structure and reducibility of braids”, J. Algebra, 356:1 (2012), 355–373  crossref  mathscinet  zmath  isi  scopus
    2. Caruso S., “A family of pseudo-Anosov braids whose super-summit sets grow exponentially”, J. Knot Theory Ramifications, 22:9 (2013), 1350050  crossref  mathscinet  zmath  isi  scopus
    3. An Byung Hee, Ko Ki Hyoung, “A family of pseudo-Anosov braids with large conjugacy invariant sets”, J. Knot Theory Ramifications, 22:6 (2013), 1350025, 20 pp.  crossref  mathscinet  zmath  isi  scopus
    4. M. Calvez, “Fast Nielsen-Thurston classification of braids”, Algebr. Geom. Topol., 14:3 (2014), 1745–1758  crossref  mathscinet  zmath  isi  scopus
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