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Diffeomorphism type of six-dimensional cohomogeneity one manifolds

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Abstract

In this article, we give a full diffeomorphism characterization of compact simply connected cohomogeneity one manifolds in dimension 6.

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References

  1. Cleyton R., Swann A.: Cohomogeneity-one G 2-structures. J. Geom. Phys. 44, 202 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Conti D.: Cohomogeneity one Einstein–Sasaki 5-manifolds. Commun. Math. Phys 274(3), 751–774 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cvetic M., Gibbons G.W., Lu H., Pope C.N.: New cohomogeneity one metrics with spin(7) Holonomy. J. Geom. Phys. 49, 350–365 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gibbons G.W., Hartnoll S.A., Yasui Y.: Properties of some five dimensional Einstein metrics. Classical Quantum Gravity 21, 4697–4730 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Grove, K., Vardiani, L., Ziller, W.: A positively curved manifold homeomorphic to T 1 S 4, arXiv:0809.2304v3 [math.DG]

  6. Grove K., Wilking B., Ziller W.: Positively curved cohomogeneity one manifolds and 3-Sasakian geometry. J. Differential Geom 78(1), 33–111 (2008)

    MATH  MathSciNet  Google Scholar 

  7. Grove K., Ziller W.: Curvature and symmetry of Milnor spheres. Ann. Math. 152, 331–367 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Grove K., Ziller W.: Cohomogeneity one manifolds with positive Ricci curvature. Invent. Math. 149, 619–646 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hoelscher, C.A.: Classification of cohomogeneity one manifolds in low dimensions, arXiv:0712.1327v1 [math.DG]

  10. Hoelscher, C.A.: On the homology of low dimensional cohomogeneity one manifolds, to appear in Transformation Groups

  11. Mimura M., Toda H.: Topology of Lie groups, I and II. Translations of Mathematical Monographs, vol. 91. American Mathematical Society, Providence, RI (1991)

    Google Scholar 

  12. Neumann W.D.: 3-Dimensional G-manifolds with 2-dimensional orbits. In: Mostert, P.S. (eds) Proceedings of Conference on Transformation Groups, pp. 220–222. Springer Verlag, Berlin (1968)

    Google Scholar 

  13. Parker J.: 4-Dimensional G-manifolds with 3-dimensional orbits. Pacific J. Math. 129(1), 187–204 (1986)

    Google Scholar 

  14. Steenrod N.: The Topology of Fibre Bundles. Princeton University Press, Princeton (1951)

    MATH  Google Scholar 

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Correspondence to Corey A. Hoelscher.

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Hoelscher, C.A. Diffeomorphism type of six-dimensional cohomogeneity one manifolds. Ann Glob Anal Geom 38, 1–9 (2010). https://doi.org/10.1007/s10455-010-9196-2

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  • DOI: https://doi.org/10.1007/s10455-010-9196-2

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