Geometry & Topology Volume 23, issue 3 (2019)

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Infinite loop spaces and positive scalar curvature in the presence of a fundamental group

Johannes Ebert and Oscar Randal-Williams

Geometry & Topology 23 (2019) 1549–1610

DOI: 10.2140/gt.2019.23.1549

Bibliography

1	D W Anderson, E H Brown Jr., F P Peterson, The structure of the Spin cobordism ring, Ann. of Math. 86 (1967) 271 MR0219077
2	N Bárcenas, R Zeidler, Positive scalar curvature and low-degree group homology, Ann. K–Theory 3 (2018) 565 MR3830202
3	P Baum, M Karoubi, On the Baum–Connes conjecture in the real case, Q. J. Math. 55 (2004) 231 MR2082090
4	R Bieri, Homological dimension of discrete groups, Department of Pure Mathematics, Queen Mary College (1981) MR715779
5	B Blackadar, K–theory for operator algebras, 5, Cambridge Univ. Press (1998) MR1656031
6	B Botvinnik, J Ebert, O Randal-Williams, Infinite loop spaces and positive scalar curvature, Invent. Math. 209 (2017) 749 MR3681394
7	B Botvinnik, P B Gilkey, The eta invariant and metrics of positive scalar curvature, Math. Ann. 302 (1995) 507 MR1339924
8	L Buggisch, The spectral flow theorem for families of twisted Dirac operators, PhD thesis, Westfälische Wilhelms-Universität Münster (2019)
9	U Bunke, A K–theoretic relative index theorem and Callias-type Dirac operators, Math. Ann. 303 (1995) 241 MR1348799
10	V Chernysh, On the homotopy type of the space ℛ⁺(M), preprint (2004) arXiv:math/0405235
11	V Chernysh, A quasifibration of spaces of positive scalar curvature metrics, Proc. Amer. Math. Soc. 134 (2006) 2771 MR2213758
12	A Connes, G Skandalis, The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sci. 20 (1984) 1139 MR775126
13	J Dixmier, A Douady, Champs continus d’espaces hilbertiens et de C^∗–algèbres, Bull. Soc. Math. France 91 (1963) 227 MR0163182
14	J Ebert, Elliptic regularity for Dirac operators on families of noncompact manifolds, preprint (2016) arXiv:1608.01699
15	J Ebert, The two definitions of the index difference, Trans. Amer. Math. Soc. 369 (2017) 7469 MR3683115
16	J Ebert, Index theory in spaces of manifolds, Math. Ann. (2019)
17	J. Ebert, O. Randal-Williams, The positive scalar curvature cobordism category, preprint (2019) arXiv:1904.12951
18	S Echterhoff, Bivariant KK–theory and the Baum–Connes conjecture, from: "K–theory for group C^∗–algebras and semigroup C^∗–algebras" (editors J Cuntz, S Echterhoff, X Li, G Yu), Oberwolfach Seminars 47, Springer (2017) 81 MR3618901
19	S Führing, A smooth variation of Baas–Sullivan theory and positive scalar curvature, Math. Z. 274 (2013) 1029 MR3078256
20	P Gajer, Riemannian metrics of positive scalar curvature on compact manifolds with boundary, Ann. Global Anal. Geom. 5 (1987) 179 MR962295
21	S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759
22	S Galatius, O Randal-Williams, Homological stability for moduli spaces of high dimensional manifolds, II, Ann. of Math. 186 (2017) 127 MR3665002
23	S Gallot, D Hulin, J Lafontaine, Riemannian geometry, Springer (2004) MR2088027
24	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
25	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
26	M Gromov, H B Lawson Jr., The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980) 423 MR577131
27	J C Hausmann, D Husemoller, Acyclic maps, Enseign. Math. 25 (1979) 53 MR543552
28	D W Henderson, Infinite-dimensional manifolds are open subsets of Hilbert space, Bull. Amer. Math. Soc. 75 (1969) 759 MR0247634
29	N Higson, J Roe, Analytic K–homology, Oxford Univ. Press (2000) MR1817560
30	N Higson, J Roe, K–homology, assembly and rigidity theorems for relative eta invariants, Pure Appl. Math. Q. 6 (2010) 555 MR2761858
31	M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
32	M Joachim, S Stolz, An enrichment of KK–theory over the category of symmetric spectra, Münster J. Math. 2 (2009) 143 MR2545610
33	D D Joyce, Compact 8–manifolds with holonomy Spin(7), Invent. Math. 123 (1996) 507 MR1383960
34	M Karoubi, A descent theorem in topological K–theory, K–Theory 24 (2001) 109 MR1869624
35	G G Kasparov, The operator K–functor and extensions of C^∗–algebras, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980) 571 MR582160
36	M A Kervaire, Le théorème de Barden–Mazur–Stallings, Comment. Math. Helv. 40 (1965) 31 MR0189048
37	M Land, The analytical assembly map and index theory, J. Noncommut. Geom. 9 (2015) 603 MR3359022
38	H B Lawson Jr., M L Michelsohn, Spin geometry, 38, Princeton Univ. Press (1989) MR1031992
39	W Lück, H Reich, The Baum–Connes and the Farrell–Jones conjectures in K– and L–theory, from: "Handbook of K–theory" (editors E M Friedlander, D R Grayson), Springer (2005) 703 MR2181833
40	M Matthey, The Baum–Connes assembly map, delocalization and the Chern character, Adv. Math. 183 (2004) 316 MR2041902
41	N Perlmutter, Parametrized Morse theory and positive scalar curvature, preprint (2017) arXiv:1705.02754
42	A Phillips, Submersions of open manifolds, Topology 6 (1967) 171 MR0208611
43	P Piazza, T Schick, Groups with torsion, bordism and rho invariants, Pacific J. Math. 232 (2007) 355 MR2366359
44	J Rosenberg, C^∗–algebras, positive scalar curvature, and the Novikov conjecture, Inst. Hautes Études Sci. Publ. Math. 58 (1983) 197 MR720934
45	T Schick, Real versus complex K–theory using Kasparov’s bivariant KK–theory, Algebr. Geom. Topol. 4 (2004) 333 MR2077669
46	T Schick, L²–index theorems, KK–theory, and connections, New York J. Math. 11 (2005) 387 MR2188248
47	S Stolz, Concordance classes of positive scalar curvature metrics, unpublished manuscript (1998)
48	C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. 81 (1965) 56 MR0171284
49	C T C Wall, Geometrical connectivity, I, J. London Math. Soc. 3 (1971) 597 MR0290387
50	M Walsh, Metrics of positive scalar curvature and generalised Morse functions, I, 983, Amer. Math. Soc. (2011) MR2789750
51	M Walsh, Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics, Proc. Amer. Math. Soc. 141 (2013) 2475 MR3043028
52	M Walsh, The space of positive scalar curvature metrics on a manifold with boundary, preprint (2014) arXiv:1411.2423
53	S Weinberger, G Yu, Finite part of operator K–theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds, Geom. Topol. 19 (2015) 2767 MR3416114
54	Z Xie, G Yu, R Zeidler, On the range of the relative higher index and the higher rho-invariant for positive scalar curvature, preprint (2017) arXiv:1712.03722