Geometriae Dedicata

, Volume 200, Issue 1, pp 265–285 | Cite as

On the cardinality of the manifold set

  • Diarmuid CrowleyEmail author
  • Tibor Macko
Original Paper


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.


Manifold set Structure set Rigidity Surgery Divisibility 

Mathematics Subject Classification (2010)

Primary: 57R65 57R67 



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


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia
  2. 2.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia

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