Volume 15, issue 1 (2011)

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Some new examples with almost positive curvature

Martin Kerin

Geometry & Topology 15 (2011) 217–260
Bibliography
1 J F Adams, Lectures on exceptional Lie groups, (Z Mahmud, M Mimura, editors) Chicago Lectures in Math., Univ. of Chicago Press (1996) MR1428422
2 S Aloff, N R Wallach, An infinite family of distinct $7$–manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc. 81 (1975) 93 MR0370624
3 Y V Bazaikin, On a family of $13$–dimensional closed Riemannian manifolds of positive curvature, Sibirsk. Mat. Zh. 37 (1996) 1219 MR1440379
4 M Berger, Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive, Ann. Scuola Norm. Sup. Pisa $(3)$ 15 (1961) 179 MR0133083
5 A Borel, F Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958) 458 MR0102800
6 E H Brown Jr., The cohomology of $B\mathrm{SO}_{n}$ and $B\mathrm{O}_{n}$ with integer coefficients, Proc. Amer. Math. Soc. 85 (1982) 283 MR652459
7 M Čadek, M Mimura, J Vanžura, The cohomology rings of real Stiefel manifolds with integer coefficients, J. Math. Kyoto Univ. 43 (2003) 411 MR2051031
8 O Dearricott, A $7$–manifold with positive curvature, Preprint (2008)
9 J H Eschenburg, Cohomology of biquotients, Manuscripta Math. 75 (1992) 151 MR1160094
10 J H Eschenburg, M Kerin, Almost positive curvature on the Gromoll–Meyer sphere, Proc. Amer. Math. Soc. 136 (2008) 3263 MR2407092
11 M Feshbach, The integral cohomology rings of the classifying spaces of $\mathrm{O}(n)$ and $\mathrm{SO}(n)$, Indiana Univ. Math. J. 32 (1983) 511 MR703281
12 H Gluck, F Warner, W Ziller, The geometry of the Hopf fibrations, Enseign. Math. $(2)$ 32 (1986) 173 MR874686
13 D Gromoll, W Meyer, An exotic sphere with nonnegative sectional curvature, Ann. of Math. $(2)$ 100 (1974) 401 MR0375151
14 K Grove, L Verdiani, W Ziller, An exotic $\T_1 ^h^4$ with positive curvature, Preprint (2008)
15 K Grove, W Ziller, Lifting group actions and non-negative curvature, to appear in Trans. Amer. Math. Soc. arXiv:0801.0767
16 N Jacobson, Composition algebras and their automorphisms, Rend. Circ. Mat. Palermo $(2)$ 7 (1958) 55 MR0101253
17 M Kerin, On the curvature of biquotients, to appear in Math. Ann.
18 M Mimura, H Toda, Topology of Lie groups. I, II, Translations of Math. Monogr. 91, Amer. Math. Soc. (1991) MR1122592
19 S Murakami, Exceptional simple Lie groups and related topics in recent differential geometry, from: "Differential geometry and topology (Tianjin, 1986–87)" (editors B J Jiang, C K Peng, Z X Hou), Lecture Notes in Math. 1369, Springer (1989) 183 MR1001187
20 P Petersen, F Wilhelm, An exotic sphere with positive sectional curvature arXiv:0805.0812
21 P Petersen, F Wilhelm, Examples of Riemannian manifolds with positive curvature almost everywhere, Geom. Topol. 3 (1999) 331 MR1714915
22 W Singhof, On the topology of double coset manifolds, Math. Ann. 297 (1993) 133 MR1238411
23 E H Spanier, Algebraic topology, Springer (1981) MR666554
24 K Tapp, Quasi-positive curvature on homogeneous bundles, J. Differential Geom. 65 (2003) 273 MR2058263
25 K Tapp, Flats in Riemannian submersions from Lie groups, Asian J. Math. 13 (2009) 459 MR2653712
26 N R Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. $(2)$ 96 (1972) 277 MR0307122
27 G W Whitehead, Elements of homotopy theory, Graduate Texts in Math. 61, Springer (1978) MR516508
28 F Wilhelm, An exotic sphere with positive curvature almost everywhere, J. Geom. Anal. 11 (2001) 519 MR1857856
29 B Wilking, Manifolds with positive sectional curvature almost everywhere, Invent. Math. 148 (2002) 117 MR1892845
30 W Ziller, Examples of Riemannian manifolds with non-negative sectional curvature, from: "Surveys in differential geometry. Vol. XI" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, Int. Press (2007) 63 MR2408264