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Mat. Zametki, 1996, Volume 60, Issue 2, Pages 163–175 (Mi mz1816)  

This article is cited in 8 scientific papers (total in 8 papers)

Obstructions to splitting manifolds with infinite fundamental group

P. M. Akhmet'ev, Yu. V. Muranov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper we calculate the obstruction groups to splitting along one-sided submanifolds when the fundamental group of the submanifold is isomorphic to $\mathbb Z$ or $\mathbb Z\oplus\mathbb Z/2$. We also consider the case where the obstruction group is not a Browder–Livesey group. We construct a new Levine braid that connects the Wall groups to the obstruction group for splitting. We solve the problem of the mutual disposition of images of several natural maps in Wall groups for finite 2-groups with exceptional orientation character.

DOI: https://doi.org/10.4213/mzm1816

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English version:
Mathematical Notes, 1996, 60:2, 121–129

Bibliographic databases:

UDC: 515.14
Received: 22.04.1994

Citation: P. M. Akhmet'ev, Yu. V. Muranov, “Obstructions to splitting manifolds with infinite fundamental group”, Mat. Zametki, 60:2 (1996), 163–175; Math. Notes, 60:2 (1996), 121–129

Citation in format AMSBIB
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\by P.~M.~Akhmet'ev, Yu.~V.~Muranov
\paper Obstructions to splitting manifolds with infinite fundamental group
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 2
\pages 163--175
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\crossref{https://doi.org/10.4213/mzm1816}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1429118}
\zmath{https://zbmath.org/?q=an:0905.57020}
\transl
\jour Math. Notes
\yr 1996
\vol 60
\issue 2
\pages 121--129
\crossref{https://doi.org/10.1007/BF02305175}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WE97100019}


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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, D. Repovš, “Spherical fibrations and $L$-groups”, Russian Math. Surveys, 54:2 (1999), 445–447  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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  scopus  scopus
    3. 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
    4. 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
    5. Cavicchioli, A, “Algebraic properties of decorated splitting obstruction groups”, Bollettino Della Unione Matematica Italiana, 4B:3 (2001), 647  mathscinet  zmath  isi
    6. 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
    7. 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
    8. 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
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