Invariable generation of certain groups of piecewise linear homeomorphisms of the interval
Authors:
Yoshifumi Matsuda and Shigenori Matsumoto
Journal:
Proc. Amer. Math. Soc. 149 (2021), 1-11
MSC (2010):
Primary 20F65; Secondary 20F05
DOI:
https://doi.org/10.1090/proc/15277
Published electronically:
October 9, 2020
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the group of all the orientation preserving piecewise linear homeomorphisms of the interval
. Given any
, let
be the subgroup of
consisting of all the elements with slopes in
, and let
be the subgroup of
consisting of all the elements with slopes and breaks in
. We show that the groups
,
,
, as well as Thompson group
, are invariably generated.
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Additional Information
Yoshifumi Matsuda
Affiliation:
Department of Physics and Mathematics, College of Science and Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa, 252-5258 Japan
Email:
ymatsuda@gem.aoyama.ac.jp
Shigenori Matsumoto
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan
Email:
matsumo@math.cst.nihon-u.ac.jp
DOI:
https://doi.org/10.1090/proc/15277
Keywords:
Invariable generation,
piecewise linear homeomorphism,
Thompson group
Received by editor(s):
August 18, 2018
Received by editor(s) in revised form:
September 4, 2018, September 20, 2019, and March 11, 2020
Published electronically:
October 9, 2020
Additional Notes:
The first author was partially supported by Grant-in-Aid for Scientific Research (C) No. 17K05260.
The second author was partially supported by Grant-in-Aid for Scientific Research (C) No. 18K03312.
Communicated by:
Kenneth Bromberg
Article copyright:
© Copyright 2020
American Mathematical Society