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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 6, Pages 107–132 (Mi izv55)  

This article is cited in 20 scientific papers (total in 20 papers)

Splitting obstruction groups and quadratic extensions of anti-structures

Yu. V. Muranov

Vitebsk State Technological University

Abstract: A natural generalization is given of the LS groups of obstructions to splitting in the case of one-sided manifolds. These LS groups depend functorially on four anti-structures and maps between them, generating a square of a special form. The connection between the LS groups and the Wall groups of anti-structures involved in the diagram is studied. “Intermediate” LS groups (LS with decorations) are also defined, by analogy with the corresponding Wall groups, and the connection between LS groups with different decorations is studied.

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English version:
Izvestiya: Mathematics, 1995, 59:6, 1207–1232

Bibliographic databases:

MSC: Primary 57R67, 57Q10, 55P10, 19J25, 19G24; Secondary 57R10, 55U35, 18F25
Received: 17.11.1994

Citation: Yu. V. Muranov, “Splitting obstruction groups and quadratic extensions of anti-structures”, Izv. RAN. Ser. Mat., 59:6 (1995), 107–132; Izv. Math., 59:6 (1995), 1207–1232

Citation in format AMSBIB
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\yr 1995
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\issue 6
\pages 107--132
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\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 6
\pages 1207--1232
\crossref{https://doi.org/10.1070/IM1995v059n06ABEH000055}
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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, “Groups of obstructions to surgery and splitting for a manifold pair”, Sb. Math., 188:3 (1997), 449–463  mathnet  crossref  crossref  mathscinet  zmath  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. 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
    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. Muranov Y. Repovs D., “Algebraic Properties of Decorated Splitting Obstruction Groups”, Boll. Unione Mat. Italiana, 4B:3 (2001), 647–675  mathscinet  zmath  isi
    7. Ruini B., Spaggiari F., “On the Computation of l-Groups and Natural Maps”, Abh. Math. Semin. Univ. Hamburg, 72 (2002), 297–308  crossref  mathscinet  zmath  isi
    8. 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
    9. Yu. V. Muranov, R. Jimenez, “Structure sets of triples of manifolds”, J. Math. Sci., 144:5 (2007), 4468–4483  mathnet  crossref  mathscinet  zmath  elib
    10. Cavicchioli A. Muranov Y. Spaggiari F., “Relative Groups in Surgery Theory”, Bull. Belg. Math. Soc.-Simon Steven, 12:1 (2005), 109–135  mathscinet  zmath  isi
    11. 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
    12. 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
    13. Cencelj M., Muranov Yu.V., Repovs D., “On the Splitting Problem for Manifold Pairs with Boundaries”, Abh. Math. Semin. Univ. Hamburg, 76 (2006), 35–55  crossref  mathscinet  zmath  isi
    14. Cavicchioli A., Muranov Yu.V., Spaggiari F., “Mixed Structures on a Manifold with Boundary”, Glasg. Math. J., 48:Part 1 (2006), 125–143  crossref  mathscinet  zmath  isi
    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. Cencelj M., Muranov Yu.V., Repovs D., “On Structure Sets of Manifold Pairs”, Homol. Homotopy Appl., 11:2 (2009), 195–222  mathscinet  zmath  isi
    18. Bak A., Muranov Y.V., “Surgery on a Pair of Transversal Manifolds”, J. Homotopy Relat. Struct., 7:2 (2012), 255–279  crossref  mathscinet  zmath  isi
    19. Muranov Yu.V. Jimenez R., “Splitting Obstruction Groups Along one-Sided Submanifolds”, Ukr. Math. J., 66:3 (2014), 352–370  crossref  mathscinet  zmath  isi  elib  scopus
    20. Jimenez R., Muranov Yu.V., “Surgery on a Stratified Space”, Mediterr. J. Math., 11:3 (2014), 979–998  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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