#### Volume 15, issue 4 (2015)

 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