Geometry & Topology Volume 30, issue 8 (2026)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Filling radius, quantitative $K$-theory and positive scalar curvature

Jinmin Wang, Zhizhang Xie, Guoliang Yu and Bo Zhu

Geometry & Topology 30 (2026) 2961–2992

DOI: 10.2140/gt.2026.30.2961

Bibliography

1	P Baum, A Connes, Geometric K-theory for Lie groups and foliations, Enseign. Math. (2) 46 (2000) 3 MR1769535
2	G Bell, A Dranishnikov, Asymptotic dimension in Będlewo, Topology Proc. 38 (2011) 209 MR2725304
3	B Blackadar, K-theory for operator algebras, 5, Cambridge Univ. Press (1998) MR1656031
4	S Y Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975) 289 MR378001
5	O Chodosh, C Li, Generalized soap bubbles and the topology of manifolds with positive scalar curvature, Ann. of Math. (2) 199 (2024) 707 MR4713021
6	A Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985) 41 MR823176
7	A Connes, Noncommutative geometry, Academic (1994) MR1303779
8	A N Dranishnikov, Macroscopic dimension and essential manifolds, Tr. Mat. Inst. Steklova 273 (2011) 41 MR2893542
9	G Gong, G Yu, Volume growth and positive scalar curvature, Geom. Funct. Anal. 10 (2000) 821 MR1791141
10	L W Green, Auf Wiedersehensflächen, Ann. of Math. (2) 78 (1963) 289 MR155271
11	M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
12	M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, II" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
13	M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser (2007) MR2307192
14	M Gromov, A dozen problems, questions and conjectures about positive scalar curvature, from: "Foundations of mathematics and physics one century after Hilbert" (editor J Kouneiher), Springer (2018) 135 MR3822551
15	M Gromov, Metric inequalities with scalar curvature, Geom. Funct. Anal. 28 (2018) 645 MR3816521
16	M Gromov, No metrics with positive scalar curvatures on aspherical 5-manifolds, (2020) arXiv:2009.05332
17	M Gromov, Four lectures on scalar curvature, from: "Perspectives in scalar curvature, I" (editors M L Gromov, J Lawson H. Blaine), World Sci. (2023) 1 MR4577903
18	M Gromov, Scalar curvature, injectivity radius and immersions with small second fundamental forms, J. Assoc. Math. Res. 3 (2025) 27 MR4876228
19	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
20	E Guentner, R Willett, G Yu, Dynamical complexity and controlled operator K-theory, 451, Société Mathématique de France (2024) 89 MR4793582
21	H Guo, V Mathai, H Wang, Positive scalar curvature and Poincaré duality for proper actions, J. Noncommut. Geom. 13 (2019) 1381 MR4059824
22	L Guth, The width–volume inequality, Geom. Funct. Anal. 17 (2007) 1139 MR2373013
23	L Guth, Metaphors in systolic geometry, from: "Proceedings of the International Congress of Mathematicians, II" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan Book Agency (2010) 745 MR2827817
24	L Guth, Volumes of balls in large Riemannian manifolds, Ann. of Math. (2) 173 (2011) 51 MR2753599
25	L Guth, Volumes of balls in Riemannian manifolds and Uryson width, J. Topol. Anal. 9 (2017) 195 MR3622232
26	G G Kasparov, Equivariant KK-theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241
27	G Kasparov, G Yu, The coarse geometric Novikov conjecture and uniform convexity, Adv. Math. 206 (2006) 1 MR2261750
28	Y Liokumovich, Z Wang, On the waist and width inequality in complete 3-manifolds with positive scalar curvature, Camb. J. Math. 14 (2026) 349 MR5073030
29	M Llarull, Sharp estimates and the Dirac operator, Math. Ann. 310 (1998) 55 MR1600027
30	S B Myers, Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941) 401 MR4518
31	H Oyono-Oyono, G Yu, On quantitative operator K-theory, Ann. Inst. Fourier (Grenoble) 65 (2015) 605 MR3449163
32	J Roe, Coarse cohomology and index theory on complete Riemannian manifolds, 497, Amer. Math. Soc. (1993) MR1147350
33	J Rosenberg, C^∗-algebras, positive scalar curvature, and the Novikov conjecture, Inst. Hautes Études Sci. Publ. Math. 58 (1983) 197 MR720934
34	J Rosenberg, C^∗-algebras, positive scalar curvature and the Novikov conjecture, II, from: "Geometric methods in operator algebras" (editors H Araki, E G Effros), Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech. (1986) 341 MR866507
35	J Rosenberg, C^∗-algebras, positive scalar curvature, and the Novikov conjecture, III, Topology 25 (1986) 319 MR842428
36	X Tang, R Willett, Y J Yao, Roe C^∗-algebra for groupoids and generalized Lichnerowicz vanishing theorem for foliated manifolds, Math. Z. 290 (2018) 1309 MR3856855
37	B L Wang, H Wang, Localized index and L²-Lefschetz fixed-point formula for orbifolds, J. Differential Geom. 102 (2016) 285 MR3454548
38	J Wang, Z Xie, On Gromov’s flat corner domination conjecture and Stoker’s conjecture, (2022) arXiv:2203.09511
39	J Wang, Z Xie, G Yu, On Gromov’s dihedral extremality and rigidity conjectures, (2021) arXiv:2112.01510
40	J Wang, Z Xie, G Yu, Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension, Comm. Pure Appl. Math. 77 (2024) 372 MR4666628
41	J Wang, Z Xie, G Yu, A proof of Gromov’s cube inequality on scalar curvature, J. Differential Geom. 128 (2024) 1285 MR4810224
42	R Willett, G Yu, The universal coefficient theorem for C^∗-algebras with finite complexity, 8, EMS Press (2024) MR4711665
43	G Yu, Zero-in-the-spectrum conjecture, positive scalar curvature and asymptotic dimension, Invent. Math. 127 (1997) 99 MR1423027
44	G Yu, The Novikov conjecture for groups with finite asymptotic dimension, Ann. of Math. (2) 147 (1998) 325 MR1626745
45	G Yu, The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math. 139 (2000) 201 MR1728880
46	W Zhang, Positive scalar curvature on foliations, Ann. of Math. (2) 185 (2017) 1035 MR3664818