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Surgery on pairs of closed manifolds

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Abstract

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group LP* generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the case of an elementary fundamental group. Then we generalize them, and obtain several further results about the realization of elements in the Browder-Quinn surgery obstruction groups by means of normal maps to a closed manifold filtered by closed submanifolds.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100, Modena, Italia

    Alberto Cavicchioli & Fulvia Spaggiari

  2. Physical Department, Vitebsk State University, Moskovskii pr. 33, 210026, Vitebsk, Belarus

    Yuri V. Muranov

Authors
  1. Alberto Cavicchioli
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  2. Yuri V. Muranov
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  3. Fulvia Spaggiari
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Corresponding author

Correspondence to Alberto Cavicchioli.

Additional information

Partially supported by the RFFI Grant No. 05-01-00993, by the GNSAGA of the National Research Council of Italy, by the MIUR (Ministero della Istruzione, Università e Ricerca) of Italy within the project ‘Proprietà Geometriche delle Varietà Reali e Complesse’, and by a Research Grant of the University of Modena and Reggio Emilia. The second author would like to thank the MPI (Bonn), the ICTP (Trieste), and the University of Modena and Reggio Emilia for their kind hospitality and support in different periods during the year 2007, and the Commission on Development and Exchange of IMU for the travel support.

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Cavicchioli, A., Muranov, Y.V. & Spaggiari, F. Surgery on pairs of closed manifolds. Czech Math J 59, 551–571 (2009). https://doi.org/10.1007/s10587-009-0037-z

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