Quasi-Isometry Invariants and Asymptotic Cones

We present some results about quasi-isometry invariants, particularly emphasizing the relationships between their behavior and properties of asymptotic cones. Our main objects of study are hyperbol...

[1]  D. Cooper.  A Rigidity Theorem for the Solvable Baumslag-solitar Groups , 1996 .

[2]  Equivalence of Geometric and Combinatorial Dehn Functions , 1995, dg-ga/9508008.

[3]  S. Gersten.  Quasi-isometry invariance of cohomological dimension , 1993 .

[4]  Alex Wilkie,et al.  Gromov's theorem on groups of polynomial growth and elementary logic , 1984 .

[5]  Noel Brady,et al.  There is only one gap in the isoperimetric spectrum , 2000 .

[6]  Quasi-flats in semihyperbolic groups , 1998 .

[7]  The large scale geometry of the higher Baumslag-Solitar groups , 2001, math/0405272.

[8]  R. Bieri,et al.  Almost finitely presented soluble groups , 1978 .

[9]  P. Papasoglu.  Isodiametric and Isoperimetric Inequalities for Complexes and Groups , 2000 .

[11]  B. Kleiner,et al.  Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings , 1997 .

[12]  Nondistorsion des horosphères dans des immeubles euclidiens et dans des espaces symétriques , 1997 .

[13]  M. Gromov.  Groups of polynomial growth and expanding maps , 1981 .

[14]  J. Cannon.  The combinatorial structure of cocompact discrete hyperbolic groups , 1984 .

[15]  P. Pansu,et al.  Métriques de Carnot-Carthéodory et quasiisométries des espaces symétriques de rang un , 1989 .

[16]  S. M. Gersten,et al.  THE OPTIMAL ISOPERIMETRIC INEQUALITY FOR TORUS BUNDLES OVER THE CIRCLE , 1996 .

[17]  Hyman Bass,et al.  The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups , 1972 .

[18]  REMPLISSAGE DANS DES RESEAUX DE Q-RANG 1 ET DANS DES GROUPES RESOLUBLES , 1998 .

[19]  Асимптотический подконус плоскости Лобачевского как пространство функций@@@An asymptotic subcone of the Lobachevskii plane as a space of functions , 1997 .

[20]  S. M. Gersten,et al.  Dehn functions and l1-norms of nite presentations , 1989 .

[21]  Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups , 1999, math/9911099.

[22]  Benson Farb,et al.  On the asymptotic geometry of abelian-by-cyclic groups , 2000, math/0005181.

[23]  R. Bieri,et al.  Valuations and Finitely Presented Metabelian Groups , 1980 .

[24]  Problems on the geometry of finitely generated solvable groups , 2000, math/0005184.

[25]  Panos Papasoglu.  An algorithm detecting hyperbolicity , 1994, Geometric and Computational Perspectives on Infinite Groups.

[26]  Mark V. Sapir,et al.  Algorithmic Problems in Varieties , 1995, Int. J. Algebra Comput..

[27]  M. Kapovich,et al.  On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds , 1995 .

[28]  M. Kapovich,et al.  Quasi-isometries preserve the geometric decomposition of Haken manifolds , 1997 .

[29]  Martin Bridson.  Fractional isoperimetric inequalities and subgroup distortion , 1996 .

[30]  Charles F. Miller,et al.  Isoperimetric inequalities and the homology of groups , 1993 .

[31]  J. M. Alonso.  INEGALITES ISOPERIMETRIQUES ET QUASI-ISOMETRIES , 1990 .

[32]  An isoperimetric inequality for the Heisenberg groups , 1998 .

[33]  M. Bridson,et al.  Isoperimetric inequalities for the fundamental groups of torus bundles over the circle , 1994 .

[34]  Athanase Papadopoulos,et al.  Géométrie et théorie des groupes , 1990 .

[35]  Quasi-isometric classification of non-uniform lattices in semisimple groups of higher rank , 2000 .

[36]  Asymptotic Cones of Finitely Generated Groups , 2000 .

[37]  S. M. Gersten,et al.  Geometric Group Theory: Isoperimetric and Isodiametric Functions of Finite Presentations , 1993 .

[38]  Benson Farb,et al.  Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II , 1998, math/9809010.

[39]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[40]  G. Mostow.  Strong Rigidity of Locally Symmetric Spaces. , 1973 .

[41]  S. J. Pride,et al.  Higher dimensional isoperimetric (or Dehn) functions of groups , 1999 .

[42]  J. Milnor.  Growth of finitely generated solvable groups , 1968 .

[43]  P. Pansu.  Croissance des boules et des géodésiques fermées dans les nilvariétés , 1983, Ergodic Theory and Dynamical Systems.

[44]  Brian H. Bowditch,et al.  A short proof that a subquadratic isoperimetric inequality implies a linear one. , 1995 .

[45]  C. Pittet,et al.  Isoperimetric Inequalities for Homogeneous Nilpotent Groups , 1995 .

[46]  Isoperimetric Inequalities in Nilpotent Groups , 1997 .

[47]  Filling in solvable groups and in lattices in semisimple groups , 2001, math/0110107.

[48]  T. Riley.  Higher connectedness of asymptotic cones , 2003 .

[49]  Benson Farb,et al.  A rigidity theorem for the solvable Baumslag-Solitar groups , 1998 .

[50]  J. Wolf.  Growth of finitely generated solvable groups and curvature of Riemannian manifolds , 1968 .

[51]  P. Papasoglu.  On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality , 1996 .

[52]  F. Paulin.  Topologie de Gromov équivariante, structures hyperboliques et arbres réels , 1988 .