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Mathematische Annalen

, Volume 370, Issue 1–2, pp 669–726 | Cite as

Approximately fibering a manifold over an aspherical one

  • Tom Farrell
  • Wolfgang Lück
  • Wolfgang SteimleEmail author
Article

Abstract

The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to manifold approximate fibration. We define obstructions in algebraic K-theory. Their vanishing is necessary and under certain conditions sufficient. Basic ingredients are Quinn’s thin h-cobordism theorem and end theorem, and knowledge about the Farrell–Jones conjectures in algebraic K- and L-theory and the MAF-rigidity conjecture by Hughes–Taylor–Williams.

Mathematics Subject Classification

55R65 19J10 

Notes

Acknowledgements

This paper is financially supported by the Leibniz-Preis of the second author, granted by the Deutsche Forschungsgemeinschaft DFG. Moreover the first named author was partially supported by NSF Grant DMS-1206622. The third named author was partly supported by the ERC Advanced Grant 288082 and by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). We thank the referee for his detailed report and very valuable comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Tom Farrell
    • 1
    • 2
  • Wolfgang Lück
    • 3
  • Wolfgang Steimle
    • 4
    Email author
  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  3. 3.Mathematisches InstitutUniversität BonnBonnGermany
  4. 4.Institut für MathematikUniversität AugsburgAugsburgGermany

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