Structure sets of triples of manifolds
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The structure set of a given manifold fits into a surgery exact sequence, which is the main tool for classification of manifolds. In the present paper, we describe relations between various structure sets and groups of obstructions which naturally arise for triples of manifolds. The main results are given by commutative braids and diagrams of exact sequences.
KeywordsManifold Exact Sequence Fundamental Group Commutative Diagram Spectrum Level
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- 3.W. Browder and F. Quinn, “A surgery theory for G-manifolds and stratified spaces,” in: Manifolds, Univ. of Tokyo Press (1975), pp. 27–36.Google Scholar
- 6.I. Hambleton, “Projective surgery obstructions on closed manifolds,” in: Algebraic K-Theory, Proc. Conf., Oberwolfach 1980, Part II, Lect. Notes Math., Vol. 967, Springer, Berlin (1982), 101–131.Google Scholar
- 8.I. Hambleton and E. Pedersen, Topological Equivalences of Linear Representations for Cyclic Groups, preprint, MPI (1997).Google Scholar
- 13.J. Malešič, Yu. V. Muranov, and D. Repovš, “Splitting obstruction groups in codimension 2,” Mat. Zametki, 69, 52–73 (2001).Google Scholar
- 16.Yu. V. Muranov and R. Jimenez, “Transfer maps for triples of manifolds,” Mat. Zametki, to appear.Google Scholar
- 19.Yu. V. Muranov, D. Repovš, and R. Jimenez, “Surgery spectral sequence and stratified manifolds,” in: Preprint of the University of Ljubljana, Vol. 42, No. 935, 2004, pp. 1–33.Google Scholar
- 21.A. A. Ranicki, Exact Sequences in the Algebraic Theory of Surgery, Math. Notes, Vol. 26, Princeton Univ. Press, Princeton (1981).Google Scholar
- 23.A. A. Ranicki, Algebraic L-Theory and Topological Manifolds, Cambridge Tracts Math., Cambridge Univ. Press (1992).Google Scholar
- 24.R. Switzer, Algebraic Topology—Homotopy and Homology, Grund. Math. Wiss., Bd. 212, Springer Berlin (1975).Google Scholar
- 25.C. T. C. Wall, Surgery on Compact Manifolds, Academic Press, London (1970). Second Edition: A. A. Ranicki, ed., AMS, Providence (1999).Google Scholar