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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 3307766
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: P. Nowak and G. Yu
Title: Large scale geometry
Additional book information: EMS Textbooks in Mathematics, European Mathematical Society, Z\"urich, 2012, xiv+189 pp., ISBN 978-3-03719-112-5, \geneuro{}38.00, $41.80

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  • Tim Austin, Amenable groups with very poor compression into Lebesgue spaces, Duke Math. J. 159 (2011), no. 2, 187–222. MR 2824482, DOI 10.1215/00127094-1415860
  • Tim Austin, Assaf Naor, and Yuval Peres, The wreath product of $\Bbb Z$ with $\Bbb Z$ has Hilbert compression exponent $\frac {2}{3}$, Proc. Amer. Math. Soc. 137 (2009), no. 1, 85–90. MR 2439428, DOI 10.1090/S0002-9939-08-09501-4
  • A. Bartels, On proofs of the Farrell-Jones Conjecture, arXiv:1210.1044
  • Laurent Bartholdi and Bálint Virág, Amenability via random walks, Duke Math. J. 130 (2005), no. 1, 39–56. MR 2176547, DOI 10.1215/S0012-7094-05-13012-5
  • B. Bekka, P. de la Harpe and A. Valette, Kazhdan’s property $(T)$. New Mathematical Monographs, 11. Cambridge University Press, Cambridge, 2008.
  • Jonathan Block and Shmuel Weinberger, Large scale homology theories and geometry, Geometric topology (Athens, GA, 1993) AMS/IP Stud. Adv. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1997, pp. 522–569. MR 1470747, DOI 10.1090/amsip/002.1/30
  • J. Bourgain, On Lipschitz embedding of finite metric spaces in Hilbert space, Israel J. Math. 52 (1985), no. 1-2, 46–52. MR 815600, DOI 10.1007/BF02776078
  • Robert Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981), no. 4, 581–598. MR 656213, DOI 10.1007/BF02566228
  • Dmitri Burago, Yuri Burago, and Sergei Ivanov, A course in metric geometry, Graduate Studies in Mathematics, vol. 33, American Mathematical Society, Providence, RI, 2001. MR 1835418, DOI 10.1090/gsm/033
  • Stanley Chang and Shmuel Weinberger, On invariants of Hirzebruch and Cheeger-Gromov, Geom. Topol. 7 (2003), 311–319. MR 1988288, DOI 10.2140/gt.2003.7.311
  • Jeff Cheeger and Bruce Kleiner, Differentiating maps into $L^1$, and the geometry of BV functions, Ann. of Math. (2) 171 (2010), no. 2, 1347–1385. MR 2630066, DOI 10.4007/annals.2010.171.1347
  • M. Coornaert, T. Delzant, and A. Papadopoulos, Géométrie et théorie des groupes, Lecture Notes in Mathematics, vol. 1441, Springer-Verlag, Berlin, 1990 (French). Les groupes hyperboliques de Gromov. [Gromov hyperbolic groups]; With an English summary. MR 1075994
  • Persi Diaconis, The Markov chain Monte Carlo revolution, Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 2, 179–205. MR 2476411, DOI 10.1090/S0273-0979-08-01238-X
  • Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg, A history and survey of the Novikov conjecture, Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993) London Math. Soc. Lecture Note Ser., vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 7–66. MR 1388295, DOI 10.1017/CBO9780511662676.003
  • Erling Følner, On groups with full Banach mean value, Math. Scand. 3 (1955), 243–254. MR 79220, DOI 10.7146/math.scand.a-10442
  • Steve M. Gersten, Quasi-isometry invariance of cohomological dimension, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 5, 411–416 (English, with English and French summaries). MR 1209258
  • E. Ghys and P. de la Harpe, Sur les groupes hyperboliques d’après Mikhael Gromov. (French) Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988. Progress in Mathematics, 83. Birkhäuser Boston, Inc., Boston, MA, 1990
  • M. Gromov,
  • Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534
  • Misha Gromov, Metric structures for Riemannian and non-Riemannian spaces, Reprint of the 2001 English edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2007. Based on the 1981 French original; With appendices by M. Katz, P. Pansu and S. Semmes; Translated from the French by Sean Michael Bates. MR 2307192
  • 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
  • M. Gromov, Random walk in random groups, Geom. Funct. Anal. 13 (2003), no. 1, 73–146. MR 1978492, DOI 10.1007/s000390300002
  • 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}
  • Mikhael Gromov and H. Blaine Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 83–196 (1984). MR 720933
  • Erik Guentner, Nigel Higson, and Shmuel Weinberger, The Novikov conjecture for linear groups, Publ. Math. Inst. Hautes Études Sci. 101 (2005), 243–268. MR 2217050, DOI 10.1007/s10240-005-0030-5
  • Erik Guentner, Romain Tessera, and Guoliang Yu, A notion of geometric complexity and its application to topological rigidity, Invent. Math. 189 (2012), no. 2, 315–357. MR 2947546, DOI 10.1007/s00222-011-0366-z
  • Juha Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917, DOI 10.1007/978-1-4613-0131-8
  • Nigel Higson and Gennadi Kasparov, $E$-theory and $KK$-theory for groups which act properly and isometrically on Hilbert space, Invent. Math. 144 (2001), no. 1, 23–74. MR 1821144, DOI 10.1007/s002220000118
  • N. Higson, V. Lafforgue, and G. Skandalis, Counterexamples to the Baum-Connes conjecture, Geom. Funct. Anal. 12 (2002), no. 2, 330–354. MR 1911663, DOI 10.1007/s00039-002-8249-5
  • Shlomo Hoory, Nathan Linial, and Avi Wigderson, Expander graphs and their applications, Bull. Amer. Math. Soc. (N.S.) 43 (2006), no. 4, 439–561. MR 2247919, DOI 10.1090/S0273-0979-06-01126-8
  • D. A. Každan, On the connection of the dual space of a group with the structure of its closed subgroups, Funkcional. Anal. i Priložen. 1 (1967), 71–74 (Russian). MR 0209390
  • Harry Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336–354. MR 109367, DOI 10.1090/S0002-9947-1959-0109367-6
  • Alex Kontorovich, From Apollonius to Zaremba: local-global phenomena in thin orbits, Bull. Amer. Math. Soc. (N.S.) 50 (2013), no. 2, 187–228. MR 3020826, DOI 10.1090/S0273-0979-2013-01402-2
  • E. Kowalski, The large sieve and its applications, Cambridge Tracts in Mathematics, vol. 175, Cambridge University Press, Cambridge, 2008. Arithmetic geometry, random walks and discrete groups. MR 2426239, DOI 10.1017/CBO9780511542947
  • Vincent Lafforgue, La conjecture de Baum-Connes à coefficients pour les groupes hyperboliques, J. Noncommut. Geom. 6 (2012), no. 1, 1–197 (French, with English and French summaries). MR 2874956, DOI 10.4171/JNCG/89
  • Nathan Linial, Eran London, and Yuri Rabinovich, The geometry of graphs and some of its algorithmic applications, Combinatorica 15 (1995), no. 2, 215–245. MR 1337355, DOI 10.1007/BF01200757
  • Alexander Lubotzky, Discrete groups, expanding graphs and invariant measures, Progress in Mathematics, vol. 125, Birkhäuser Verlag, Basel, 1994. With an appendix by Jonathan D. Rogawski. MR 1308046, DOI 10.1007/978-3-0346-0332-4
  • Alexander Lubotzky, Expander graphs in pure and applied mathematics, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 113–162. MR 2869010, DOI 10.1090/S0273-0979-2011-01359-3
  • Wolfgang Lück, $K$- and $L$-theory of group rings, Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, New Delhi, 2010, pp. 1071–1098. MR 2827832
  • G. A. Margulis, Explicit constructions of expanders, Problemy Peredači Informacii 9 (1973), no. 4, 71–80 (Russian). MR 0484767
  • John Milnor, Growth of finitely generated solvable groups, J. Differential Geometry 2 (1968), 447–449. MR 244899
  • Igor Mineyev and Guoliang Yu, The Baum-Connes conjecture for hyperbolic groups, Invent. Math. 149 (2002), no. 1, 97–122. MR 1914618, DOI 10.1007/s002220200214
  • G. D. Mostow, Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53–104. MR 236383
  • Assaf Naor, $L_1$ embeddings of the Heisenberg group and fast estimation of graph isoperimetry, Proceedings of the International Congress of Mathematicians. Volume III, Hindustan Book Agency, New Delhi, 2010, pp. 1549–1575. MR 2827855
  • Alexander Yu. Ol′shanskii and Mark V. Sapir, Non-amenable finitely presented torsion-by-cyclic groups, Publ. Math. Inst. Hautes Études Sci. 96 (2002), 43–169 (2003). MR 1985031
  • Pierre Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2) 129 (1989), no. 1, 1–60 (French, with English summary). MR 979599, DOI 10.2307/1971484
  • John Roe, Lectures on coarse geometry, University Lecture Series, vol. 31, American Mathematical Society, Providence, RI, 2003. MR 2007488, DOI 10.1090/ulect/031
  • John Roe, Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. 104 (1993), no. 497, x+90. MR 1147350, DOI 10.1090/memo/0497
  • Jonathan Rosenberg, $C^{\ast }$-algebras, positive scalar curvature, and the Novikov conjecture, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 197–212 (1984). MR 720934
  • R. Sauer, Homological invariants and quasi-isometry, Geom. Funct. Anal. 16 (2006), no. 2, 476–515. MR 2231471, DOI 10.1007/s00039-006-0562-y
  • R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), no. 1-3, 159–183. MR 535700, DOI 10.1007/BF01647970
  • Yehuda Shalom, The algebraization of Kazhdan’s property (T), International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1283–1310. MR 2275645
  • G. Skandalis, J. L. Tu, and G. Yu, The coarse Baum-Connes conjecture and groupoids, Topology 41 (2002), no. 4, 807–834. MR 1905840, DOI 10.1016/S0040-9383(01)00004-0
  • John R. Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. (2) 88 (1968), 312–334. MR 228573, DOI 10.2307/1970577
  • Alain Valette, Nouvelles approches de la propriété (T) de Kazhdan, Astérisque 294 (2004), vii, 97–124 (French, with French summary). MR 2111641
  • N. Th. Varopoulos, L. Saloff-Coste, and T. Coulhon, Analysis and geometry on groups, Cambridge Tracts in Mathematics, vol. 100, Cambridge University Press, Cambridge, 1992. MR 1218884
  • S. Weinberger, Variations on a theme of Borel (to appear)
  • Kevin Whyte, Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture, Duke Math. J. 99 (1999), no. 1, 93–112. MR 1700742, DOI 10.1215/S0012-7094-99-09904-0
  • Guoliang Yu, Higher index theory of elliptic operators and geometry of groups, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1623–1639. MR 2275662
  • Guoliang Yu, The Novikov conjecture for groups with finite asymptotic dimension, Ann. of Math. (2) 147 (1998), no. 2, 325–355. MR 1626745, DOI 10.2307/121011
  • Guoliang Yu, The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math. 139 (2000), no. 1, 201–240. MR 1728880, DOI 10.1007/s002229900032
  • A. Żuk, Property (T) and Kazhdan constants for discrete groups, Geom. Funct. Anal. 13 (2003), no. 3, 643–670. MR 1995802, DOI 10.1007/s00039-003-0425-8

  • Review Information:

    Reviewer: Shmuel Weinberger
    Affiliation: Department of Mathematics, University of Chicago
    Journal: Bull. Amer. Math. Soc. 52 (2015), 141-149
    Published electronically: August 20, 2014
    Review copyright: © Copyright 2014 American Mathematical Society