Geometry & Topology Volume 17, issue 1 (2013)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

On the Hopf conjecture with symmetry

Lee Kennard

Geometry & Topology 17 (2013) 563–593

DOI: 10.2140/gt.2013.17.563

Bibliography

1	J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20 MR0141119
2	J Adem, The iteration of the Steenrod squares in algebraic topology, Proc. Nat. Acad. Sci. U. S. A. 38 (1952) 720 MR0050278
3	M Berger, Trois remarques sur les variétés riemanniennes à courbure positive, C. R. Acad. Sci. Paris Sér. A-B 263 (1966) MR0199823
4	R L Bishop, S I Goldberg, Some implications of the generalized Gauss–Bonnet theorem, Trans. Amer. Math. Soc. 112 (1964) 508 MR0163271
5	S s Chern, On curvature and characteristic classes of a Riemann manifold, Abh. Math. Sem. Univ. Hamburg 20 (1955) 117 MR0075647
6	P E Conner, On the action of the circle group, Michigan Math. J. 4 (1957) 241 MR0096747
7	O Dearricott, A 7-manifold with positive curvature, Duke Math. J. 158 (2011) 307 MR2805071
8	K Grove, Developments around positive sectional curvature, from: "Surveys in differential geometry. Vol. XIII. Geometry, analysis, and algebraic geometry : forty years of the Journal of Differential Geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 13, International Press (2009) 117 MR2537084
9	K Grove, L Verdiani, W Ziller, An exotic T₁𝕊⁴ with positive curvature, Geom. Funct. Anal. 21 (2011) 499 MR2810857
10	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
11	A Liulevicius, The factorization of cyclic reduced powers by secondary cohomology operations, Mem. Amer. Math. Soc. No. 42 (1962) 112 MR0182001
12	P Petersen, F Wilhelm, An exotic sphere with positive curvature arXiv:0805.0812v3
13	T Püttmann, C Searle, The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank, Proc. Amer. Math. Soc. 130 (2002) 163 MR1855634
14	X Rong, X Su, The Hopf conjecture for manifolds with abelian group actions, Commun. Contemp. Math. 7 (2005) 121 MR2129791
15	N Shimada, T Yamanoshita, On triviality of the mod p Hopf invariant, Japan J. Math. 31 (1961) 1 MR0148060
16	X Su, Y Wang, The Hopf conjecture for positively curved manifolds with discrete abelian group actions, Differential Geom. Appl. 26 (2008) 313 MR2421709
17	B Wilking, Torus actions on manifolds of positive sectional curvature, Acta Math. 191 (2003) 259 MR2051400
18	B Wilking, Positively curved manifolds with symmetry, Ann. of Math. 163 (2006) 607 MR2199227
19	B Wilking, Nonnegatively and positively curved manifolds, from: "Surveys in differential geometry. Vol. XI" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, International Press (2007) 25 MR2408263
20	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, International Press (2007) 63 MR2408264