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Mat. Sb., 1990, Volume 181, Number 8, Pages 1061–1098 (Mi msb1209)  

This article is cited in 19 scientific papers (total in 19 papers)

Browder–Livesay groups for Abelian 2-groups

Yu. V. Muranov, A. F. Kharshiladze

Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation

Abstract: The authors compute all the Browder–Livesay groups of an arbitrary finite abelian 2-group with an arbitrary orientation character and any subgroup of index 2. Browder–Livesay groups are obstruction groups for the problem of splitting homotopy equivalences of manifolds along one-sided submanifolds of codimension 1. All the connections with the Wall groups of abelian 2-groups which can be expressed by two-row diagrams are uncovered.

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English version:
Mathematics of the USSR-Sbornik, 1991, 70:2, 499–540

Bibliographic databases:

UDC: 515.16
MSC: Primary 57R67; Secondary 57R65, 18F25
Received: 30.05.1989

Citation: Yu. V. Muranov, A. F. Kharshiladze, “Browder–Livesay groups for Abelian 2-groups”, Mat. Sb., 181:8 (1990), 1061–1098; Math. USSR-Sb., 70:2 (1991), 499–540

Citation in format AMSBIB
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\by Yu.~V.~Muranov, A.~F.~Kharshiladze
\paper Browder--Livesay groups for Abelian 2-groups
\jour Mat. Sb.
\yr 1990
\vol 181
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\pages 1061--1098
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\transl
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\yr 1991
\vol 70
\issue 2
\pages 499--540
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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, “The Browder–Livesay groups of the dihedral group”, Russian Math. Surveys, 47:2 (1992), 231–232  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. Hambleton, A. F. Kharshiladze, “A spectral sequence in surgery”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 1–9  mathnet  crossref  mathscinet  zmath  isi
    3. Yu. V. Muranov, “Natural mappings of relative Wall groups”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 183–195  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. V. Muranov, “Tate cohomologies and Browder–Livesay groups of dihedral groups”, Math. Notes, 54:2 (1993), 798–805  mathnet  crossref  mathscinet  zmath  isi
    5. Yu. V. Muranov, “$K$-groups of quadratic extensions of rings”, Math. Notes, 58:2 (1995), 861–866  mathnet  crossref  mathscinet  zmath  isi
    6. Yu. V. Muranov, “Splitting obstruction groups and quadratic extensions of anti-structures”, Izv. Math., 59:6 (1995), 1207–1232  mathnet  crossref  mathscinet  zmath  isi
    7. P. M. Akhmet'ev, Yu. V. Muranov, “Obstructions to splitting manifolds with infinite fundamental group”, Math. Notes, 60:2 (1996), 121–129  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Yu. V. Muranov, D. Repovš, “Groups of obstructions to surgery and splitting for a manifold pair”, Sb. Math., 188:3 (1997), 449–463  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. 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
    10. 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
    11. 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
    12. 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
    13. Yu. V. Muranov, R. Jimenez, “Structure sets of triples of manifolds”, J. Math. Sci., 144:5 (2007), 4468–4483  mathnet  crossref  mathscinet  zmath  elib
    14. Cavicchioli, A, “Relative groups in surgery theory”, Bulletin of the Belgian Mathematical Society-Simon Stevin, 12:1 (2005), 109  mathscinet  zmath  isi  elib
    15. 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
    16. 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
    17. Cavicchioli, A, “Assembly maps and realization of splitting obstructions”, Monatshefte fur Mathematik, 158:4 (2009), 367  crossref  mathscinet  zmath  isi
    18. Cavicchioli, A, “SURGERY ON PAIRS OF CLOSED MANIFOLDS”, Czechoslovak Mathematical Journal, 59:2 (2009), 551  crossref  mathscinet  isi  elib
    19. Muranov Yu.V. Jimenez R., “Splitting Obstruction Groups Along One-Sided Submanifolds”, Ukr. Math. J., 66:3 (2014), 352–370  crossref  isi
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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