Algebraic & Geometric Topology Volume 14, issue 1 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

To Appear

Other MSP Journals

Asymptotic cones of HNN extensions and amalgamated products

Curtis Kent

Algebraic & Geometric Topology 14 (2014) 551–595

DOI: 10.2140/agt.2014.14.551

Bibliography

1	M R Bridson, D Groves, The quadratic isoperimetric inequality for mapping tori of free group automorphisms, Mem. Amer. Math. Soc. 955 (2010) MR2590896
2	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer (1999) MR1744486
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	D J Collins, J Huebschmann, Spherical diagrams and identities among relations, Math. Ann. 261 (1982) 155 MR675732
7	G Conner, C Kent, Local topological properties of asymptotic cones of groups arXiv:1210.4411
8	Y Cornulier, R Tessera, Dehn function and asymptotic cones of Abels' group, J. Topol. 6 (2013)
9	N DeJarnette, P Hajlasz, A Lukyanenko, J Tyson, On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target arXiv:1109.4641
10	C Druţu, S Mozes, M V Sapir, Divergence in lattices in semisimple Lie groups and graphs of groups, Trans. Amer. Math. Soc. 362 (2010) 2451 MR2584607
11	C Druţu, M V Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
12	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 (1992) MR1161694
13	A Erschler, D V Osin, Fundamental groups of asymptotic cones, Topology 44 (2005) 827 MR2136537
14	R Geoghegan, The shape of a group — connections between shape theory and the homology of groups, from: "Geometric and algebraic topology" (editors H Toruńczyk, S Jackowski, S Spie), Banach Center Publ. 18 (1986) 271 MR925870
15	H B Griffiths, The fundamental group of two spaces with a common point: A correction, Quart. J. Math. Oxford Ser. 6 (1955) 154 MR0070167
16	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
17	V S Guba, The Dehn function of Richard Thompson's group $F$ is quadratic, Invent. Math. 163 (2006) 313 MR2207020
18	W Hurewicz, H Wallman, Dimension theory, Princeton Mathematical Series 4, Princeton Univ. Press (1941) MR0006493
19	L Kramer, S Shelah, K Tent, S Thomas, Asymptotic cones of finitely presented groups, Adv. Math. 193 (2005) 142 MR2132762
20	L Mosher, Mapping class groups are automatic, Ann. of Math. 142 (1995) 303 MR1343324
21	J R Munkres, Topology: A first course, Prentice-Hall (1975) MR0464128
22	A Y Ol’shanskii, Geometry of defining relations in groups, Mathematics and its Applications (Soviet Series) 70, Kluwer (1991) MR1191619
23	A Y Ol’shanskii, D V Osin, M V Sapir, Lacunary hyperbolic groups, Geom. Topol. 13 (2009) 2051 MR2507115
24	A Y Ol’shanskii, M V Sapir, Groups with non-simply connected asymptotic cones, from: "Topological and asymptotic aspects of group theory", Contemp. Math. 394, Amer. Math. Soc. (2006) 203 MR2216717
25	A Y Ol’shanskii, M V Sapir, Groups with small Dehn functions and bipartite chord diagrams, Geom. Funct. Anal. 16 (2006) 1324 MR2276542
26	A Y Ol’shanskii, M V Sapir, A finitely presented group with two non-homeomorphic asymptotic cones, Internat. J. Algebra Comput. 17 (2007) 421 MR2310154
27	D V Osin, M V Sapir, Universal tree-graded spaces and asymptotic cones, Internat. J. Algebra Comput. 21 (2011) 793 MR2827204
28	P Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergodic Theory Dynam. Systems 3 (1983) 415 MR741395
29	P Papasoglu, On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality, J. Differential Geom. 44 (1996) 789 MR1438192
30	F Point, Groups of polynomial growth and their associated metric spaces, J. Algebra 175 (1995) 105 MR1338969
31	M V Sapir, J C Birget, E Rips, Isoperimetric and isodiametric functions of groups, Ann. of Math. 156 (2002) 345 MR1933723
32	A Sisto, Tree-graded asymptotic cones, Groups Geom. Dyn. 7 (2013) 697 MR3095715
33	R Young, The Dehn function of $\mathrm{SL}(n;\mathbb Z)$, Ann. of Math. 177 (2013) 969 MR3034292