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

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

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
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
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