Geometry & Topology Volume 17, issue 3 (2013)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The Gromoll filtration, $\mathit{KO}$–characteristic classes and metrics of positive scalar curvature

Diarmuid Crowley and Thomas Schick

Geometry & Topology 17 (2013) 1773–1789

DOI: 10.2140/gt.2013.17.1773

Bibliography

1	J F Adams, On the groups J(X), IV, Topology 5 (1966) 21 MR0198470
2	P Antonelli, D Burghelea, P J Kahn, Gromoll groups, DiffSⁿ and bilinear constructions of exotic spheres, Bull. Amer. Math. Soc. 76 (1970) 772 MR0283809
3	B Botvinnik, P B Gilkey, The eta invariant and metrics of positive scalar curvature, Math. Ann. 302 (1995) 507 MR1339924
4	D Burghelea, On the homotopy type of diff(Mⁿ) and connected problems, Ann. Inst. Fourier (Grenoble) 23 (1973) 3 MR0380840
5	D Burghelea, R Lashof, The homotopy type of the space of diffeomorphisms, I, II, Trans. Amer. Math. Soc. 196 (1974) 1, 37 MR0356103
6	J Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Publ. Math. (1970) 5 MR0292089
7	E B Curtis, Some nonzero homotopy groups of spheres, Bull. Amer. Math. Soc. 75 (1969) 541 MR0245007
8	D Gromoll, Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären, Math. Ann. 164 (1966) 353 MR0196754
9	B Hanke, T Schick, W Steimle, The space of metrics of positive scalar curvature arXiv:1212.0068
10	A E Hatcher, A proof of the Smale conjecture, Diff(S³) ≃ O(4), Ann. of Math. 117 (1983) 553 MR701256
11	M W Hirsch, B Mazur, Smoothings of piecewise linear manifolds, 80, Princeton Univ. Press (1974) MR0415630
12	N Hitchin, Harmonic spinors, Advances in Math. 14 (1974) 1 MR0358873
13	M A Kervaire, J W Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963) 504 MR0148075
14	R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, 88, Princeton Univ. Press (1977) MR0645390
15	T Lance, Differentiable structures on manifolds, from: "Surveys on surgery theory, Vol. 1" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 145, Princeton Univ. Press (2000) 73 MR1747531
16	R Lashof, M Rothenberg, Microbundles and smoothing, Topology 3 (1965) 357 MR0176480
17	H B Lawson Jr., M L Michelsohn, Spin geometry, 38, Princeton Univ. Press (1989) MR1031992
18	J P Levine, Lectures on groups of homotopy spheres, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 62 MR802786
19	W Lück, A basic introduction to surgery theory, from: "Topology of high-dimensional manifolds, No. 1, 2" (editors F T Farrell, L Göttsche, W Lück), ICTP Lect. Notes 9, Abdus Salam Int. Cent. Theoret. Phys., Trieste (2002) 1 MR1937016
20	I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, 92, Princeton Univ. Press (1979) MR548575
21	J W Milnor, Remarks concerning spin manifolds, from: "Differential and Combinatorial Topology", Princeton Univ. Press (1965) 55 MR0180978
22	S P Novikov, Differentiable sphere bundles, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965) 71 MR0174059
23	P Piazza, T Schick, Groups with torsion, bordism and rho invariants, Pacific J. Math. 232 (2007) 355 MR2366359
24	J Rosenberg, C^∗–algebras, positive scalar curvature, and the Novikov conjecture, Inst. Hautes Études Sci. Publ. Math. (1983) 197 MR720934
25	T Schick, A counterexample to the (unstable) Gromov–Lawson–Rosenberg conjecture, Topology 37 (1998) 1165 MR1632971
26	S Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. 74 (1961) 391 MR0137124
27	S Stolz, Simply connected manifolds of positive scalar curvature, Ann. of Math. 136 (1992) 511 MR1189863
28	H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR0143217
29	M Weiss, Sphères exotiques et l’espace de Whitehead, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986) 885 MR870913
30	M Weiss, Pinching and concordance theory, J. Differential Geom. 38 (1993) 387 MR1237489