Volume 14, issue 3 (2014)

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Local topological properties of asymptotic cones of groups

Gregory R Conner and Curtis Kent

Algebraic & Geometric Topology 14 (2014) 1413–1439
Bibliography
1 M R Bridson, Asymptotic cones and polynomial isoperimetric inequalities, Topology 38 (1999) 543 MR1670404
2 M R Bridson, K Vogtmann, The Dehn functions of $\mathrm{Out}(F_n)$ and $\mathrm{Aut}(F_n)$, Ann. Inst. Fourier (Grenoble) 62 (2012) 1811 MR3025154
3 J Burillo, Dimension and fundamental groups of asymptotic cones, J. London Math. Soc. 59 (1999) 557 MR1709665
4 J W Cannon, G R Conner, The combinatorial structure of the Hawaiian earring group, Topology Appl. 106 (2000) 225 MR1775709
5 J W Cannon, G R Conner, On the fundamental groups of one-dimensional spaces, Topology Appl. 153 (2006) 2648 MR2243740
6 Y de Cornulier, Dimension of asymptotic cones of Lie groups, J. Topol. 1 (2008) 342 MR2399134
7 C Druţu, Quasi-isometry invariants and asymptotic cones, Internat. J. Algebra Comput. 12 (2002) 99 MR1902363
8 C Druţu, M V Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
9 K Eda, Atomic property of the fundamental groups of the Hawaiian earring and wild locally path-connected spaces, J. Math. Soc. Japan 63 (2011) 769 MR2836742
10 D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett Publishers (1992) MR1161694
11 A Erschler, D V Osin, Fundamental groups of asymptotic cones, Topology 44 (2005) 827 MR2136537
12 S M Gersten, Dehn functions and $l_1$–norms of finite presentations, from: "Algorithms and classification in combinatorial group theory" (editor G Baumslag), Math. Sci. Res. Inst. Publ. 23, Springer (1992) 195 MR1230635
13 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
14 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
15 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
16 G Higman, Unrestricted free products, and varieties of topological groups, J. London Math. Soc. 27 (1952) 73 MR0045730
17 M Kassabov, T R Riley, The Dehn function of Baumslag's metabelian group, arXiv:1008.1966
18 C Kent, Asymptotic cones of HNN–extensions and amalgamated products
19 A Y Olshanskii, Groups with quadratic-non-quadratic Dehn functions, Internat. J. Algebra Comput. 17 (2007) 401 MR2310153
20 A Y Olshanskii, D V Osin, M V Sapir, Lacunary hyperbolic groups, Geom. Topol. 13 (2009) 2051 MR2507115
21 A Y Olshanskii, M V Sapir, Groups with non-simply connected asymptotic cones, from: "Topological and asymptotic aspects of group theory" (editors R Grigorchuk, M Mihalik, M V Sapir, Z Šunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 203 MR2216717
22 A Y Olshanskii, M V Sapir, A finitely presented group with two non-homeomorphic asymptotic cones, Internat. J. Algebra Comput. 17 (2007) 421 MR2310154
23 P Papasoglu, On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality, J. Differential Geom. 44 (1996) 789 MR1438192
24 A N Platonov, An isoparametric function of the Baumslag–Gersten group, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (2004) 12, 70 MR2127449
25 T R Riley, Higher connectedness of asymptotic cones, Topology 42 (2003) 1289 MR1981358
26 M V Sapir, J C Birget, E Rips, Isoperimetric and isodiametric functions of groups, Ann. of Math. 156 (2002) 345 MR1933723
27 E Summers, There is no surjective map from the Hawaiian earring group to the double Hawaiian earring group, master’s thesis, Brigham Young University (2002)
28 S Thomas, B Velickovic, Asymptotic cones of finitely generated groups, Bull. London Math. Soc. 32 (2000) 203 MR1734187