American Mathematical Society

Book Review

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MathSciNet review: 3891928
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Book Information:

Authors: Yves Cornulier and Pierre de la Harpe
Title: Metric geometry of locally compact groups
Additional book information: Tracts in Mathematics, Vol. 25, European Mathematical Society (EMS), Z\"urich, 2016, viii+235 pp., ISBN 978-3-03719-166-8

Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486, DOI 10.1007/978-3-662-12494-9

Professor Cayley, Desiderata and Suggestions: No. 2. The Theory of Groups: Graphical Representation, Amer. J. Math. 1 (1878), no. 2, 174–176. MR 1505159, DOI 10.2307/2369306

Pierre-Emmanuel Caprace, Yves Cornulier, Nicolas Monod, and Romain Tessera, Amenable hyperbolic groups, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 11, 2903–2947. MR 3420526, DOI 10.4171/JEMS/575

Yves Cornulier and Pierre de la Harpe, Metric geometry of locally compact groups, EMS Tracts in Mathematics, vol. 25, European Mathematical Society (EMS), Zürich, 2016. Winner of the 2016 EMS Monograph Award. MR 3561300, DOI 10.4171/166

Yves Cornulier and Romain Tessera, Geometric presentations of Lie groups and their Dehn functions, Publ. Math. Inst. Hautes Études Sci. 125 (2017), 79–219. MR 3668649, DOI 10.1007/s10240-016-0087-3

Max Dehn, Papers on group theory and topology, Springer-Verlag, New York, 1987. Translated from the German and with introductions and an appendix by John Stillwell; With an appendix by Otto Schreier. MR 881797, DOI 10.1007/978-1-4612-4668-8

Anna Dyubina, Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups, Internat. Math. Res. Notices 21 (2000), 1097–1101. MR 1800990, DOI 10.1155/S1073792800000544

B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no. 5, 810–840. MR 1650094, DOI 10.1007/s000390050075

Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534

M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}

M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR 1253544

Avinoam Mann, How groups grow, London Mathematical Society Lecture Note Series, vol. 395, Cambridge University Press, Cambridge, 2012. MR 2894945

D. Osin, Acylindrically hyperbolic groups, Trans. Amer. Math. Soc. 368 (2016), no. 2, 851–888. MR 3430352, DOI 10.1090/tran/6343

John Roe, Lectures on coarse geometry, University Lecture Series, vol. 31, American Mathematical Society, Providence, RI, 2003. MR 2007488, DOI 10.1090/ulect/031

Yehuda Shalom, Harmonic analysis, cohomology, and the large-scale geometry of amenable groups, Acta Math. 192 (2004), no. 2, 119–185. MR 2096453, DOI 10.1007/BF02392739

Review Information:

Reviewer: V. Nekrashevych
Affiliation: Texas A&M University, College Station, Texas
Email: nekrash@math.tamu.edu