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Mather Invariants in Groups of Piecewise-linear Homeomorphisms

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Book cover Combinatorial and Geometric Group Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [3] and Kassabov and Matucci in [6]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows us to easily recover centralizers and lends itself to generalization.

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References

  1. J.M. Belk and F. Matucci. Dynamics in Thompson’s group F. Submitted. arXiv:math.GR/0710.3633v1.

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  2. R. Bieri and R. Strebel. On groups of PL-homeomorphisms of the real line. notes, 1985. Math. Sem. der Univ. Frankfurt.

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  3. Matthew G. Brin and Craig C. Squier. Presentations, conjugacy, roots, and centralizers in groups of piecewise linear homeomorphisms of the real line. Comm. Algebra, 29(10):4557–4596, 2001.

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  4. N. Gill and I. Short. Conjugacy, roots, and centralizers in Thompson’s group F. Preprint. arXiv:math.GR/0709.1987v2.

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  5. Victor Guba and Mark Sapir. Diagram groups. Mem. Amer. Math. Soc., 130(620): viii + 117, 1997.

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  6. M. Kassabov and F. Matucci. The simultaneous conjugacy problem in groups of piecewise linear functions. preprint. arXiv:math.GR/0607167v2.

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  7. John N. Mather. Commutators of diffeomorphisms. Comment. Math. Helv., 49:512–528, 1974.

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  8. Melanie Stein. Groups of piecewise linear homeomorphisms. Trans. Amer. Math. Soc., 332(2):477–514, 1992.

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Author information

Authors and Affiliations

  1. Centre de Recerca Matemàtica, Apartat 50, E-08193, Bellaterra, Barcelona, Spain

    Francesco Matucci

Authors
  1. Francesco Matucci
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Editor information

Editors and Affiliations

  1. Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Oleg Bogopolski

  2. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Inna Bumagin

  3. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St., West, Montreal, Quebec, H3A 2K6, Canada

    Olga Kharlampovich

  4. Departament de Matematica Aplicada III, EPSEM — Universitat Politècnica de Catalunya, Av. Bases de Manresa 61-73, 08242, Manresa, Barcelona, Spain

    Enric Ventura

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Matucci, F. (2010). Mather Invariants in Groups of Piecewise-linear Homeomorphisms. In: Bogopolski, O., Bumagin, I., Kharlampovich, O., Ventura, E. (eds) Combinatorial and Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9911-5_10

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