Download this article
 Download this article For screen
For printing
Recent Issues

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Classifying sufficiently connected PSC manifolds in $4$ and $5$ dimensions

Otis Chodosh, Chao Li and Yevgeny Liokumovich

Geometry & Topology 27 (2023) 1635–1655
Bibliography
1 H Alpert, A Balitskiy, L Guth, Macroscopic scalar curvature and codimension 2 width, preprint (2021) arXiv:2112.04594
2 D Bolotov, About the macroscopic dimension of certain PSC-manifolds, Algebr. Geom. Topol. 9 (2009) 21 MR2471130
3 D Bolotov, A Dranishnikov, On Gromov’s scalar curvature conjecture, Proc. Amer. Math. Soc. 138 (2010) 1517 MR2578547
4 S Brendle, Ricci flow with surgery on manifolds with positive isotropic curvature, Ann. of Math. 190 (2019) 465 MR3997128
5 S Brendle, R Schoen, Manifolds with 14–pinched curvature are space forms, J. Amer. Math. Soc. 22 (2009) 287 MR2449060
6 B L Chen, S H Tang, X P Zhu, Complete classification of compact four-manifolds with positive isotropic curvature, J. Differential Geom. 91 (2012) 41 MR2944961
7 O Chodosh, C Li, Generalized soap bubbles and the topology of manifolds with positive scalar curvature, preprint (2020) arXiv:2008.11888
8 M J Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985) 449 MR807066
9 D B A Epstein, Ends, from: "Topology of 3–manifolds and related topics" (editor M K Fort Jr.), Prentice-Hall (1962) 110 MR0158380
10 A M Fraser, Fundamental groups of manifolds with positive isotropic curvature, Ann. of Math. 158 (2003) 345 MR1999925
11 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357 MR679066
12 S Gadgil, H Seshadri, On the topology of manifolds with positive isotropic curvature, Proc. Amer. Math. Soc. 137 (2009) 1807 MR2470841
13 M Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, from: "Functional analysis on the eve of the 21st century, II" (editors S Gindikin, J Lepowsky, R L Wilson), Progr. Math. 132, Birkhäuser (1996) 1 MR1389019
14 M Gromov, No metrics with positive scalar curvatures on aspherical 5–manifolds, preprint (2020) arXiv:2009.05332
15 M Gromov, Four lectures on scalar curvature, preprint (2021) arXiv:1908.10612v5
16 M Gromov, H B Lawson Jr., Spin and scalar curvature in the presence of a fundamental group, I, Ann. of Math. 111 (1980) 209 MR569070
17 M Gromov, H B Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983) 83 MR720933
18 R S Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997) 1 MR1456308
19 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
20 H Huang, Compact manifolds of dimension n 12 with positive isotropic curvature, preprint (2019) arXiv:1909.12265
21 M Katz, The first diameter of 3–manifolds of positive scalar curvature, Proc. Amer. Math. Soc. 104 (1988) 591 MR962834
22 M Kreck, W Lück, Topological rigidity for non-aspherical manifolds, Pure Appl. Math. Q. 5 (2009) 873 MR2532709
23 Y Liokumovich, D Maximo, Waist inequality for 3–manifolds with positive scalar curvature, preprint (2020) arXiv:2012.12478
24 F C Marques, A Neves, Rigidity of min-max minimal spheres in three-manifolds, Duke Math. J. 161 (2012) 2725 MR2993139
25 M J Micallef, J D Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. 127 (1988) 199 MR924677
26 J Milnor, Lectures on the h–cobordism theorem, Princeton Univ. Press (1965) MR0190942
27 H T Nguyen, Isotropic curvature and the Ricci flow, Int. Math. Res. Not. 2010 (2010) 536 MR2587576
28 M Ramachandran, J Wolfson, Fill radius and the fundamental group, J. Topol. Anal. 2 (2010) 99 MR2646991
29 R Schoen, Manifolds with poinwise 14-pinched curvature, preprint (2007)
30 P Scott, T Wall, Topological methods in group theory, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137 MR564422
31 J P Serre, Trees, Springer (2003) MR1954121