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Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 829–853 | Cite as

Cohomogeneity one topological manifolds revisited

  • Fernando Galaz-García
  • Masoumeh Zarei
Article
  • 136 Downloads

Abstract

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply-connected cohomogeneity one topological manifolds in dimensions 5, 6, and 7 and obtain topological characterizations of these spaces. In these dimensions, these manifolds are homeomorphic to smooth manifolds.

Keywords

Topological manifold Cohomogeneity one Group action Smoothing 

Mathematics Subject Classification

57S10 57M60 57S25 57R10 57N15 

Notes

Acknowledgements

M. Zarei thanks the Institut für Algebra und Geometrie at the Karlsruher Institut für Technologie (KIT) for its hospitality while the work presented herein was carried out. Both authors would like to thank Anand Dessai, Marco Radeschi and Alexey V. Zhubr for helpful conversations on the proof of Theorem G, and Martin Herrmann, Wilderich Tuschmann and Burkhard Wilking for conversations on the smoothability of manifolds. The authors also thank Martin Kerin, Wolfgang Ziller and the referee for suggesting improvements to the exposition. M. Zarei was partially supported by the Ministry of Science, Research and Technology of Iran.

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Authors and Affiliations

  1. 1.Institut für Algebra und Geometrie Karlsruher Institut für Technologie (KIT)KarlsruheGermany
  2. 2.Department of Pure Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran

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