Volume 15, issue 4 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Positive curvature and rational ellipticity

Manuel Amann and Lee Kennard

Algebraic & Geometric Topology 15 (2015) 2269–2301
Bibliography
1 C Allday, V Puppe, Cohomological methods in transformation groups, Cambridge Studies in Advanced Mathematics 32, Cambridge Univ. Press (1993) MR1236839
2 M Amann, Positive quaternion Kähler manifolds, PhD thesis, Westfälische Wilhelms–Universität Münster (2009)
3 M Amann, L Kennard, Topological properties of positively curved manifolds with symmetry, Geom. Funct. Anal. 24 (2014) 1377 MR3261629
4 I Belegradek, V Kapovitch, Obstructions to nonnegative curvature and rational homotopy theory, J. Amer. Math. Soc. 16 (2003) 259 MR1949160
5 M Berger, Sur quelques variétés riemanniennes suffisamment pincées, Bull. Soc. Math. France 88 (1960) 57 MR0133781
6 A Blanchard, Sur les variétés analytiques complexes, Ann. Sci. Ecole Norm. Sup. 73 (1956) 157 MR0087184
7 C Böhm, B Wilking, Manifolds with positive curvature operators are space forms, Ann. of Math. 167 (2008) 1079 MR2415394
8 W Browder, Fiberings of spheres and $H$–spaces which are rational homology spheres, Bull. Amer. Math. Soc. 68 (1962) 202 MR0148071
9 X Chen, Curvature and Riemannian submersions, PhD thesis, University of Notre Dame (2014)
10 O Dearricott, A $7$–manifold with positive curvature, Duke Math. J. 158 (2011) 307 MR2805071
11 J H Eschenburg, Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekrümmten Orbiträumen, Schriftenr. Math. Inst. Univ. Münster (II) 32, Mathematisches Institut (1984) MR758252
12 Y Félix, S Halperin, J C Thomas, Rational homotopy theory, Graduate Texts in Mathematics 205, Springer (2001) MR1802847
13 Y Félix, J Oprea, D Tanré, Algebraic models in geometry, Oxford Graduate Texts in Mathematics 17, Oxford Univ. Press (2008) MR2403898
14 L A Florit, W Ziller, Topological obstructions to fatness, Geom. Topol. 15 (2011) 891 MR2821566
15 D Gromoll, K Grove, A generalization of Berger's rigidity theorem for positively curved manifolds, Ann. Sci. École Norm. Sup. 20 (1987) 227 MR911756
16 K Grove, Geometry of, and via, symmetries, from: "Conformal, Riemannian and Lagrangian geometry" (editor A Freire), Univ. Lecture Ser. 27, Amer. Math. Soc. (2002) 31 MR1922721
17 K Grove, Developments around positive sectional curvature, from: "Geometry, analysis, and algebraic geometry: forty years of the Journal of Differential Geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 13, Int. Press (2009) 117 MR2537084
18 K Grove, S Halperin, Dupin hypersurfaces, group actions and the double mapping cylinder, J. Differential Geom. 26 (1987) 429 MR910016
19 K Grove, C Searle, Positively curved manifolds with maximal symmetry-rank, J. Pure Appl. Algebra 91 (1994) 137 MR1255926
20 K Grove, L Verdiani, W Ziller, An exotic $T_1\mathbb S^4$ with positive curvature, Geom. Funct. Anal. 21 (2011) 499 MR2810857
21 S Halperin, Rational fibrations, minimal models, and fibrings of homogeneous spaces, Trans. Amer. Math. Soc. 244 (1978) 199 MR0515558
22 S Halperin, Polynomial growth and elliptic spaces, unpublished (2012)
23 I M James, editor, Handbook of algebraic topology, North-Holland (1995) MR1361885
24 L Kennard, On the Hopf conjecture with symmetry, Geom. Topol. 17 (2013) 563 MR3039770
25 L Kennard, Positively curved Riemannian metrics with logarithmic symmetry rank bounds, Comment. Math. Helv. 89 (2014) 937 MR3284301
26 M Kerin, Some new examples with almost positive curvature, Geom. Topol. 15 (2011) 217 MR2776844
27 G Lupton, Note on a conjecture of Stephen Halperin's, from: "Topology and combinatorial group theory" (editor P Latiolais), Lecture Notes in Math. 1440, Springer (1990) 148 MR1082989
28 G Lupton, Variations on a conjecture of Halperin, from: "Homotopy and geometry" (editors J Oprea, A Tralle), Banach Center Publ. 45, Polish Acad. Sci., Warsaw (1998) 115 MR1679854
29 A L Mare, M Willems, Topology of the octonionic flag manifold, Münster J. Math. 6 (2013) 483 MR3148220
30 M Markl, Towards one conjecture on collapsing of the Serre spectral sequence, from: "Proceedings of the Winter School on Geometry and Physics" (editors J Bureš, V Souček), Rend. Circ. Mat. Palermo Suppl. 22 (1990) 151 MR1061796
31 W Meier, Rational universal fibrations and flag manifolds, Math. Ann. 258 (1982) 329 MR649203
32 W Meier, Some topological properties of Kähler manifolds and homogeneous spaces, Math. Z. 183 (1983) 473 MR710764
33 S Papadima, L Paunescu, Reduced weighted complete intersection and derivations, J. Algebra 183 (1996) 595 MR1399041
34 P Petersen, F Wilhem, An exotic sphere with positive curvature, preprint (2008) arXiv:0805.0812v3
35 T Püttmann, C Searle, The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank, Proc. Amer. Math. Soc. 130 (2002) 163 MR1855634
36 X Rong, X Su, The Hopf conjecture for manifolds with abelian group actions, Commun. Contemp. Math. 7 (2005) 121 MR2129791
37 H Shiga, M Tezuka, Rational fibrations, homogeneous spaces with positive Euler characteristics and Jacobians, Ann. Inst. Fourier (Grenoble) 37 (1987) 81 MR894562
38 Z Su, Rational analogs of projective planes, Algebr. Geom. Topol. 14 (2014) 421 MR3158765
39 J C Thomas, Rational homotopy of Serre fibrations, Ann. Inst. Fourier (Grenoble) 31 (1981) 71 MR638617
40 J M Wahl, Derivations, automorphisms and deformations of quasihomogeneous singularities, from: "Singularities, Part 2" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 613 MR713285
41 N R Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. 96 (1972) 277 MR0307122
42 G Walschap, Soul-preserving submersions, Michigan Math. J. 41 (1994) 609 MR1297712
43 B Wilking, Index parity of closed geodesics and rigidity of Hopf fibrations, Invent. Math. 144 (2001) 281 MR1826371
44 B Wilking, Torus actions on manifolds of positive sectional curvature, Acta Math. 191 (2003) 259 MR2051400
45 B Wilking, Positively curved manifolds with symmetry, Ann. of Math. 163 (2006) 607 MR2199227
46 B Wilking, Nonnegatively and positively curved manifolds, from: "Metric and comparison geometry" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, Int. Press (2007) 25 MR2408263
47 J E Yeager, Geometric and topological ellipticity in cohomogeneity two, PhD thesis, University of Maryland (2012)
48 O Zariski, P Samuel, Commutative algebra, I, Graduate Texts in Mathematics 28, Springer (1975) MR0384768
49 O Zariski, P Samuel, Commutative algebra, II, Graduate Texts in Mathematics 29, Springer (1976) MR0389876
50 W Ziller, Examples of Riemannian manifolds with non-negative sectional curvature, from: "Metric and comparison geometry" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, Int. Press (2007) 63 MR2408264
51 W Ziller, Riemannian manifolds with positive sectional curvature, from: "Geometry of manifolds with non-negative sectional curvature" (editors R Herrera, L Hernández-Lamoneda), Springer (2014) 1