Algebraic & Geometric Topology Volume 22, issue 7 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Cheeger–Gromoll splitting theorem for groups

Thang Nguyen and Shi Wang

Algebraic & Geometric Topology 22 (2022) 3377–3399

DOI: 10.2140/agt.2022.22.3377

Bibliography

1	A Bar-Natan, M Duchin, R Kropholler, Conjugation curvature for Cayley graphs, J. Topol. Anal. 14 (2022) 439 MR4446915
2	I Benjamini, O Schramm, Á Timár, On the separation profile of infinite graphs, Groups Geom. Dyn. 6 (2012) 639 MR2996405
3	R L Bishop, A relation between volume, mean curvature, and diameter, Notices Amer. Math. Soc. 10 (1963) 364
4	J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, I, J. Differential Geom. 46 (1997) 406 MR1484888
5	J Cheeger, D Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry 6 (1971/72) 119 MR303460
6	J Cheeger, W Müller, R Schrader, On the curvature of piecewise flat spaces, Comm. Math. Phys. 92 (1984) 405 MR734226
7	J Cheeger, A Naber, Lower bounds on Ricci curvature and quantitative behavior of singular sets, Invent. Math. 191 (2013) 321 MR3010378
8	H Garland, p–adic curvature and the cohomology of discrete subgroups of p–adic groups, Ann. of Math. 97 (1973) 375 MR320180
9	M Gromov, Almost flat manifolds, J. Differential Geometry 13 (1978) 231 MR540942
10	M Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981) 53 MR623534
11	M Gromov, Structures métriques pour les variétés riemanniennes, 1, CEDIC (1981) MR682063
12	J Hempel, 3-Manifolds, 86, Princeton Univ. Press (1976)
13	A Keisling, Medium-scale Ricci curvature for hyperbolic groups, preprint (2021) arXiv:2101.01813
14	R Kropholler, B Mallery, Medium-scale curvature at larger radii in finitely generated groups, preprint (2020) arXiv:2004.10801
15	J Lohkamp, Metrics of negative Ricci curvature, Ann. of Math. 140 (1994) 655 MR1307899
16	J Lott, C Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. 169 (2009) 903 MR2480619
17	J Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976) 293 MR425012
18	Y Ollivier, Ricci curvature of metric spaces, C. R. Math. Acad. Sci. Paris 345 (2007) 643 MR2371483
19	Y Ollivier, Ricci curvature of Markov chains on metric spaces, J. Funct. Anal. 256 (2009) 810 MR2484937
20	Y Ollivier, A survey of Ricci curvature for metric spaces and Markov chains, from: "Probabilistic approach to geometry" (editors M Kotani, M Hino, T Kumagai), Adv. Stud. Pure Math. 57, Math. Soc. Japan (2010) 343 MR2648269
21	Y Ollivier, A visual introduction to Riemannian curvatures and some discrete generalizations, from: "Analysis and geometry of metric measure spaces" (editors G Dafni, R J McCann, A Stancu), CRM Proc. Lecture Notes 56, Amer. Math. Soc. (2013) 197 MR3060504
22	K T Sturm, On the geometry of metric measure spaces, I, Acta Math. 196 (2006) 65 MR2237206
23	K T Sturm, On the geometry of metric measure spaces, II, Acta Math. 196 (2006) 133 MR2237207
24	B Wilking, On fundamental groups of manifolds of nonnegative curvature, Differential Geom. Appl. 13 (2000) 129 MR1783960