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Mat. Sb., 2003, Volume 194, Number 8, Pages 139–160 (Mi msb764)  

This article is cited in 9 scientific papers (total in 9 papers)

Surgery on triples of manifolds

Yu. V. Muranova, D. Repovšb, F. Spaggiaric

a Vitebsk Institute of Modern Knowledge
b University of Ljubljana
c University of Modena and Reggio Emilia

Abstract: The surgery obstruction groups for a manifold pair were introduced by Wall for the study of the surgery problem on a manifold with a submanifold. These groups are closely related to the problem of splitting a homotopy equivalence along a submanifold and have been used in many geometric and topological applications.
In the present paper the concept of surgery on a triple of manifolds is introduced and algebraic and geometric properties of the corresponding obstruction groups are described. It is then shown that these groups are closely related to the normal invariants and the classical splitting and surgery obstruction groups, respectively, of the manifold in question. In the particular case of one-sided submanifolds relations between the newly introduced groups and the surgery spectral sequence constructed by Hambleton and Kharshiladze are obtained.

DOI: https://doi.org/10.4213/sm764

Full text: PDF file (331 kB)
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English version:
Sbornik: Mathematics, 2003, 194:8, 1251–1271

Bibliographic databases:

UDC: 513.8+515.1
MSC: 57R67, 57Q10, 19J25, 19G24, 18F25
Received: 11.07.2002

Citation: Yu. V. Muranov, D. Repovš, F. Spaggiari, “Surgery on triples of manifolds”, Mat. Sb., 194:8 (2003), 139–160; Sb. Math., 194:8 (2003), 1251–1271

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. V. Muranov, R. Jimenez, “Structure sets of triples of manifolds”, J. Math. Sci., 144:5 (2007), 4468–4483  mathnet  crossref  mathscinet  zmath  elib
    2. Yu. V. Muranov, R. Himenez, “Transfer maps for triples of manifolds”, Math. Notes, 79:3 (2006), 387–398  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Cavicchioli A., Muranov Yu.V., Spaggiari F., “Mixed structures on a manifold with boundary”, Glasg. Math. J., 48:1 (2006), 125–143  crossref  mathscinet  zmath  isi  elib  scopus
    4. Yu. V. Muranov, D. Repovš, M. Cencelj, “The $\pi$-$\pi$-Theorem for Manifold Pairs”, Math. Notes, 81:3 (2007), 356–364  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Jimenez R., Muranov Yu.V., Repovš D., “Splitting along a submanifold pair”, J. K-Theory, 2:2, Special issue in memory of Yurii Petrovich Solovyev, Part 1 (2008), 385–404  crossref  mathscinet  zmath  isi  scopus
    6. A. Bak, Yu. V. Muranov, “Splitting a simple homotopy equivalence along a submanifold with filtration”, Sb. Math., 199:6 (2008), 787–809  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. A. Cavicchioli, Yu. V. Muranov, F. Spaggiari, F. Hegenbarth, “On Iterated Browder–Livesay Invariants”, Math. Notes, 86:2 (2009), 196–215  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Cavicchioli A., Muranov Yu.V., Spaggiari F., “Assembly maps and realization of splitting obstructions”, Monatsh. Math., 158:4 (2009), 367–391  crossref  mathscinet  zmath  isi  elib  scopus
    9. Cavicchioli A., Muranov Yu.V., Spaggiari F., “Surgery on pairs of closed manifolds”, Czechoslovak Math. J., 59:2 (2009), 551–571  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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