On the cardinality of the manifold set

Abstract

We study the cardinality of the set of homeomorphism classes of manifolds homotopy equivalent to a given manifold M and compare it to the cardinality of the structure set of M, as defined in surgery theory.

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Acknowledgements

We would like to thank Jim Davis, Wolfgang Lück and Shmuel Weinberger for helpful and stimulating conversations.

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Correspondence to Diarmuid Crowley.

Additional information

The second author was supported by the project “Topology of high-dimensional manifolds” under the scheme “Returns” of the “Ministry of education, science, research and sport of the Slovak republic”, by the Grant VEGA 1/0101/17 and by the Slovak Research and Development Agency under the Contract No. APVV-16-0053.

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Crowley, D., Macko, T. On the cardinality of the manifold set. Geom Dedicata 200, 265–285 (2019). https://doi.org/10.1007/s10711-018-0370-1

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Keywords

  • Manifold set
  • Structure set
  • Rigidity
  • Surgery
  • Divisibility

Mathematics Subject Classification (2010)

  • Primary: 57R65
  • 57R67