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
References
- 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
- Professor Cayley, Desiderata and Suggestions: No. 2. The Theory of Groups: Graphical Representation, Amer. J. Math. 1 (1878), no. 2, 174–176. MR 1505159
- 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
- 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
- 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
- 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
- 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
- B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no. 5, 810–840. MR 1650094
- 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
- 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
- John Roe, Lectures on coarse geometry, University Lecture Series, vol. 31, American Mathematical Society, Providence, RI, 2003. MR 2007488
- Yehuda Shalom, Harmonic analysis, cohomology, and the large-scale geometry of amenable groups, Acta Math. 192 (2004), no. 2, 119–185. MR 2096453
Review Information:
Reviewer:
V. Nekrashevych
Affiliation:
Texas A&M University, College Station, Texas
Email:
nekrash@math.tamu.edu
Journal:
Bull. Amer. Math. Soc.
56 (2019), 165-169
DOI:
https://doi.org/10.1090/bull/1608
Published electronically:
January 8, 2018
Review copyright:
© Copyright 2018
American Mathematical Society