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Mat. Sb., 1997, Volume 188, Number 3, Pages 127–142 (Mi msb213)  

This article is cited in 15 scientific papers (total in 15 papers)

Groups of obstructions to surgery and splitting for a manifold pair

Yu. V. Muranova, D. Repovšb

a Vladimir State University
b University of Ljubljana

Abstract: The surgery obstruction groups $LP_*$ of manifold pairs are studied. An algebraic version of these groups for squares of antistructures of a special form equipped with decorations is considered. The squares of antistructures in question are natural generalizations of squares of fundamental groups that occur in the splitting problem for a one-sided submanifold of codimension 1 in the case when the fundamental group of the submanifold is mapped epimorphically onto the fundamental group of the manifold. New connections between the groups $LP_*$, the Novikov–Wall groups, and the splitting obstruction groups are established.

DOI: https://doi.org/10.4213/sm213

Full text: PDF file (280 kB)
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English version:
Sbornik: Mathematics, 1997, 188:3, 449–463

Bibliographic databases:

UDC: 515.1
MSC: Primary 57R67; Secondary 19J25
Received: 28.05.1996

Citation: Yu. V. Muranov, D. Repovš, “Groups of obstructions to surgery and splitting for a manifold pair”, Mat. Sb., 188:3 (1997), 127–142; Sb. Math., 188:3 (1997), 449–463

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Muranov, D. Repovš, “Spherical fibrations and $L$-groups”, Russian Math. Surveys, 54:2 (1999), 445–447  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Yu. V. Muranov, I. Hambleton, “Projective splitting obstruction groups for one-sided submanifolds”, Sb. Math., 190:10 (1999), 1465–1485  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Akhmetiev, PM, “On realization of splitting obstructions in Browder-Livesay groups for closed manifold pairs”, Proceedings of the Edinburgh Mathematical Society, 43 (2000), 15  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. I. Maleshich, Yu. V. Muranov, D. Repovš, “Splitting Obstruction Groups in Codimension 2”, Math. Notes, 69:1 (2001), 46–64  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Yu. V. Muranov, D. Repovš, “The Groups $LS$ and Morphisms of Quadratic Extensions”, Math. Notes, 70:3 (2001), 378–383  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Cavicchioli, A, “Algebraic properties of decorated splitting obstruction groups”, Bollettino Della Unione Matematica Italiana, 4B:3 (2001), 647  mathscinet  zmath  isi  elib
    7. Yu. V. Muranov, D. Repovš, “Geometric properties of a spectral sequence in surgery theory”, Russian Math. Surveys, 57:6 (2002), 1238–1239  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Ruini, B, “On the computation of L-groups and natural maps”, Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 72 (2002), 297  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Yu. V. Muranov, D. Repovš, F. Spaggiari, “Surgery on triples of manifolds”, Sb. Math., 194:8 (2003), 1251–1271  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Yu. V. Muranov, R. Jimenez, “Structure sets of triples of manifolds”, J. Math. Sci., 144:5 (2007), 4468–4483  mathnet  crossref  mathscinet  zmath  elib
    11. Cavicchioli, A, “Relative groups in surgery theory”, Bulletin of the Belgian Mathematical Society-Simon Stevin, 12:1 (2005), 109  mathscinet  zmath  isi  elib
    12. Cencelj, M, “On the splitting problem for manifold pairs with boundaries”, Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 76 (2006), 35  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    13. Cavicchioli, A, “Mixed structures on a manifold with boundary”, Glasgow Mathematical Journal, 48 (2006), 125  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    14. A. Bak, Yu. V. Muranov, “Properties of exponential series with sequence of exponents satisfying a Levinson-type condition”, Sb. Math., 197:6 (2006), 791–811  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. Muranov Yu.V. Jimenez R., “Splitting Obstruction Groups Along One-Sided Submanifolds”, Ukr. Math. J., 66:3 (2014), 352–370  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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