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Pattern rigidity and the Hilbert–Smith conjecture

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Bibliography
1 J Behrstock, C Druţu, L Mosher, Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity, Math. Ann. 344 (2009) 543 MR2501302
2 N Bergeron, D Wise, A boundary criterion for cubulation arXiv:0908.3609
3 M Bestvina, Local homology properties of boundaries of groups, Michigan Math. J. 43 (1996) 123 MR1381603
4 M Bestvina, G Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991) 469 MR1096169
5 C J Bishop, P W Jones, Hausdorff dimension and Kleinian groups, Acta Math. 179 (1997) 1 MR1484767
6 K Biswas, Flows, fixed points and rigidity in Kleinian groups, to appear in Geom. Funct. Anal. arXiv:0903.2419
7 K Biswas, M Mj, Pattern rigidity in hyperbolic spaces: duality and PD subgroups, Groups Geom. Dyn. 6 (2012) 97
8 M Bonk, B Kleiner, Quasisymmetric parametrizations of two-dimensional metric spheres, Invent. Math. 150 (2002) 127 MR1930885
9 M Bonk, O Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000) 266 MR1771428
10 M Bourdon, H Pajot, Cohomologie $l_p$ et espaces de Besov, J. Reine Angew. Math. 558 (2003) 85 MR1979183
11 B H Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998) 145 MR1638764
12 B H Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998) 643 MR1602069
13 G E Bredon, Orientation in generalized manifolds and applications to the theory of transformation groups, Michigan Math. J. 7 (1960) 35 MR0116342
14 G E Bredon, Introduction to compact transformation groups, Pure and Applied Math. 46, Academic Press (1972) MR0413144
15 G E Bredon, Sheaf theory, Graduate Texts in Math. 170, Springer (1997) MR1481706
16 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer (1999) MR1744486
17 K S Brown, Cohomology of groups, Graduate Texts in Math. 87, Springer (1994) MR1324339
18 S Buyalo, V Schroeder, Elements of asymptotic geometry, EMS Monogr. in Math., European Math. Soc. (2007) MR2327160
19 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
20 R R Coifman, G Weiss, Analyse harmonique non-commutative sur certains espaces homogènes: Étude de certaines intégrales singulières, Lecture Notes in Math. 42, Springer (1971) MR0499948
21 P E Conner, E E Floyd, A characterization of generalized manifolds, Michigan Math. J. 6 (1959) 33 MR0102818
22 M Coornaert, Mesures de Patterson–Sullivan sur le bord d'un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993) 241 MR1214072
23 M W Davis, Poincaré duality groups, from: "Surveys on surgery theory, Vol. 1" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 145, Princeton Univ. Press (2000) 167 MR1747535
24 M W Davis, T Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991) 347 MR1131435
25 K J Falconer, Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc. 106 (1989) 543 MR969315
26 B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810 MR1650094
27 É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Math. 83, Birkhäuser (1990) MR1086648
28 R Gitik, M Mitra, E Rips, M Sageev, Widths of subgroups, Trans. Amer. Math. Soc. 350 (1998) 321 MR1389776
29 A M Gleason, Groups without small subgroups, Ann. of Math. 56 (1952) 193 MR0049203
30 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
31 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2 (Sussex, 1991)" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
32 M Gromov, personal communication (2009)
33 M Gromov, W Thurston, Pinching constants for hyperbolic manifolds, Invent. Math. 89 (1987) 1 MR892185
34 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
35 J Heinonen, Lectures on analysis on metric spaces, Universitext, Springer (2001) MR1800917
36 E Hewitt, K A Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Grundl. Mathl. Wissen. 115, Academic Press (1963) MR0156915
37 J G Hocking, G S Young, Topology, Addison-Wesley (1961) MR0125557
38 T Iwaniec, G Martin, Geometric function theory and non-linear analysis, Oxford Math. Monogr., The Clarendon Press, Oxford Univ. Press (2001) MR1859913
39 M Kapovich, B Kleiner, Hyperbolic groups with low-dimensional boundary, Ann. Sci. École Norm. Sup. 33 (2000) 647 MR1834498
40 S Lefschetz, Topics in Topology, Annals of Math. Studies 10, Princeton Univ. Press (1942) MR0007094
41 J Luukkainen, E Saksman, Every complete doubling metric space carries a doubling measure, Proc. Amer. Math. Soc. 126 (1998) 531 MR1443161
42 G J Martin, The Hilbert–Smith conjecture for quasiconformal actions, Electron. Res. Announc. Amer. Math. Soc. 5 (1999) 66 MR1694197
43 J Milnor, On the Steenrod homology theory, from: "Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993)" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press (1995) 79 MR1388297
44 M Mj, Relative rigidity, quasiconvexity and $C$–complexes, Algebr. Geom. Topol. 8 (2008) 1691 MR2448868
45 D Montgomery, L Zippin, Topological transformation groups, Interscience (1955) MR0073104
46 L Mosher, M Sageev, K Whyte, Quasi-actions on trees II: Finite depth Bass–Serre trees, Mem. Amer. Math. Soc. 214 (2011) MR2867450
47 G D Mostow, Y T Siu, A compact Kähler surface of negative curvature not covered by the ball, Ann. of Math. 112 (1980) 321 MR592294
48 M H A Newman, A theorem on periodic transformation of spaces, Quart. J. Math. Oxford Ser. (2) 2 (1931) 1
49 P Pansu, Métriques de Carnot–Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989) 1 MR979599
50 F Paulin, Un groupe hyperbolique est déterminé par son bord, J. London Math. Soc. 54 (1996) 50 MR1395067
51 F Paulin, On the critical exponent of a discrete group of hyperbolic isometries, Differential Geom. Appl. 7 (1997) 231 MR1480536
52 F Raymond, R L Wilder's work on generalized manifolds—an appreciation, from: "Algebraic and geometric topology (Proc. Sympos., Univ. California, Santa Barbara, CA, 1977)" (editor K C Millett), Lecture Notes in Math. 664, Springer (1978) 7 MR518402
53 F Raymond, R F Williams, Examples of $p$–adic transformation groups, Ann. of Math. 78 (1963) 92 MR0150769
54 D Repovs, E Scepin, A proof of the Hilbert–Smith conjecture for actions by Lipschitz maps, Math. Ann. 308 (1997) 361 MR1464908
55 M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
56 R E Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. (1995) 133 MR1383215
57 R E Schwartz, Symmetric patterns of geodesics and automorphisms of surface groups, Invent. Math. 128 (1997) 177 MR1437498
58 P Scott, G A Swarup, Regular neighbourhoods and canonical decompositions for groups, Astérisque 289, Soc. Math. France (2003) MR2032389
59 P A Smith, Transformations of finite period. III: Newman's theorem, Ann. of Math. 42 (1941) 446 MR0004128
60 D Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. (1979) 171 MR556586
61 D Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984) 259 MR766265
62 G A Swarup, On the cut point conjecture, Electron. Res. Announc. Amer. Math. Soc. 2 (1996) 98 MR1412948
63 E L Swenson, On Axiom H, Michigan Math. J. 46 (1999) 3 MR1682883
64 J Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005) 187 MR2164775
65 H Yamabe, On the conjecture of Iwasawa and Gleason, Ann. of Math. 58 (1953) 48 MR0054613
66 C T Yang, Transformation groups on a homological manifold, Trans. Amer. Math. Soc. 87 (1958) 261 MR0100271
67 C T Yang, $p$–adic transformation groups, Michigan Math. J. 7 (1960) 201 MR0120310