Geometry & Topology Volume 25, issue 1 (2021)

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Positive scalar curvature on manifolds with odd order abelian fundamental groups

Bernhard Hanke

Geometry & Topology 25 (2021) 497–546

DOI: 10.2140/gt.2021.25.497

Bibliography

1	N A Baas, On bordism theory of manifolds with singularities, Math. Scand. 33 (1973) 279 MR346824
2	A L Besse, Einstein manifolds, 10, Springer (1987) MR867684
3	B Botvinnik, Manifolds with singularities and the Adams–Novikov spectral sequence, 170, Cambridge Univ. Press (1992) MR1192127
4	B Botvinnik, Manifolds with singularities accepting a metric of positive scalar curvature, Geom. Topol. 5 (2001) 683 MR1857524
5	B Botvinnik, J Rosenberg, The Yamabe invariant for non-simply connected manifolds, J. Differential Geom. 62 (2002) 175 MR1988502
6	B Botvinnik, J Rosenberg, Positive scalar curvature for manifolds with elementary abelian fundamental group, Proc. Amer. Math. Soc. 133 (2005) 545 MR2093079
7	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
8	U Bunke, Index theory, eta forms, and Deligne cohomology, 928, Amer. Math. Soc. (2009) MR2191484
9	S Eilenberg, S Mac Lane, On the groups H(Π,n), II : Methods of computation, Ann. of Math. 60 (1954) 49 MR65162
10	S Führing, A smooth variation of Baas–Sullivan theory and positive scalar curvature, Math. Z. 274 (2013) 1029 MR3078256
11	M Gromov, H B Lawson Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980) 423 MR577131
12	B Hanke, Bordism of elementary abelian groups via inessential Brown–Peterson homology, J. Topol. 9 (2016) 725 MR3551835
13	B Hanke, D Kotschick, J Wehrheim, Dissolving four-manifolds and positive scalar curvature, Math. Z. 245 (2003) 545 MR2021570
14	D C Johnson, W S Wilson, The Brown–Peterson homology of elementary p–groups, Amer. J. Math. 107 (1985) 427 MR784291
15	D Joyce, A generalization of manifolds with corners, Adv. Math. 299 (2016) 760 MR3519481
16	S Kwasik, R Schultz, Positive scalar curvature and periodic fundamental groups, Comment. Math. Helv. 65 (1990) 271 MR1057244
17	J Milnor, On the cobordism ring Ω^∗ and a complex analogue, I, Amer. J. Math. 82 (1960) 505 MR119209
18	O K Mironov, Existence of multiplicative structures in the theory of cobordism with singularities, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975) 1065 MR0402784
19	S A Mitchell, A proof of the Conner–Floyd conjecture, Amer. J. Math. 106 (1984) 889 MR749260
20	J Morava, A product for the odd-primary bordism of manifolds with singularities, Topology 18 (1979) 177 MR546788
21	S P Novikov, Some problems in the topology of manifolds connected with the theory of Thom spaces, Dokl. Akad. Nauk SSSR 132 (1960) 1031 MR0121815
22	D C Ravenel, W S Wilson, The Morava K–theories of Eilenberg–Mac Lane spaces and the Conner–Floyd conjecture, Amer. J. Math. 102 (1980) 691 MR584466
23	J Rosenberg, C^∗–algebras, positive scalar curvature, and the Novikov conjecture, III, Topology 25 (1986) 319 MR842428
24	J Rosenberg, Manifolds of positive scalar curvature: a progress report, from: "Metric and comparison geometry" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, International (2007) 259 MR2408269
25	J Rosenberg, S Stolz, Metrics of positive scalar curvature and connections with surgery, from: "Surveys on surgery theory, II" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 149, Princeton Univ. Press (2001) 353 MR1818778
26	R Schoen, S T Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979) 159 MR535700
27	N Shimada, N Yagita, Multiplications in the complex bordism theory with singularities, Publ. Res. Inst. Math. Sci. 12 (1976) 259 MR0415642
28	S Stolz, Positive scalar curvature metrics: existence and classification questions, from: "Proceedings of the International Congress of Mathematicians, I" (editor S D Chatterji), Birkhäuser (1995) 625 MR1403963
29	R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR61823