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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 5, Pages 1104–1116 (Mi izv1333)  

This article is cited in 22 scientific papers (total in 23 papers)

Transformations of special spines and the Zeeman conjecture

S. V. Matveev


Abstract: Two transformations, called elementary, are defined for special spines, and it is shown that any one special spine of aЁ3-manifold can be obtained from any other by a sequence of elementary transformations and their inverses. Applications are made to the Zeeman conjecture on 1-collapsibility of 2-dimensional contractible polyhedra.
Figures: 7.
Bibliography: 6 titles.

Full text: PDF file (1797 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1988, 31:2, 423–434

Bibliographic databases:

UDC: 515.1
MSC: Primary 57Q10; Secondary 57Q35
Received: 17.10.1985

Citation: S. V. Matveev, “Transformations of special spines and the Zeeman conjecture”, Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987), 1104–1116; Math. USSR-Izv., 31:2 (1988), 423–434

Citation in format AMSBIB
\Bibitem{Mat87}
\by S.~V.~Matveev
\paper Transformations of special spines and the Zeeman conjecture
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 5
\pages 1104--1116
\mathnet{http://mi.mathnet.ru/izv1333}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=925096}
\zmath{https://zbmath.org/?q=an:0676.57002|0642.57003}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 2
\pages 423--434
\crossref{https://doi.org/10.1070/IM1988v031n02ABEH001083}


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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. Louis H. Kauffman, Sóstenes Lins, “Computing Turaev-Viro invariants for 3-manifolds”, manuscripta math, 72:1 (1991), 81  crossref  mathscinet  zmath  isi
    2. V.G. Turaev, O.Y. Viro, “State sum invariants of 3-manifolds and quantum 6j-symbols”, Topology, 31:4 (1992), 865  crossref
    3. Vladimir Turaev, “Quantum invariants of links and 3-valent graphs in 3-manifolds”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 77:1 (1993), 121  crossref  mathscinet  zmath
    4. David N. Yetter, “State-sum invariants of 3-manifolds associated to artinian semisimple tortile categories”, Topology and its Applications, 58:1 (1994), 47  crossref
    5. Riccardo Benedetti, Carlo Petronio, “A finite graphic calculus for 3-manifolds”, manuscripta math, 88:1 (1995), 291  crossref  mathscinet  zmath  isi
    6. M. V. Sokolov, “Invariant Turaeva-Viro dlya trekhmernykh mnogoobrazii yavlyaetsya summoi trekh invariantov”, Vestnik ChelGU, 1996, no. 3, 154–162  mathnet
    7. A. Yu. Makovetskii, “Transformations of special spines and special polyhedra”, Math. Notes, 65:3 (1999), 295–301  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. M. A. Ovchinnikov, “Representation of homeotopies of a torus by simple polyhedra with a boundary”, Math. Notes, 66:4 (1999), 436–441  mathnet  crossref  crossref  mathscinet  isi
    9. A. Yu. Makovetskii, “Spainy 3-mnogoobrazii s vlozhennymi 2-komponentami”, Vestnik ChelGU, 1999, no. 4, 116–133  mathnet
    10. M. A. Ovchinnikov, “Spetsialnyi spain linzy tipa dlinnaya vosmerka i linza kak prostranstvo dvulistnogo nakrytiya 3-sfery, razvetvlennogo vdol dvumostnogo zatsepeleniya”, Vestnik ChelGU, 1999, no. 4, 145–154  mathnet
    11. Gennaro Amendola, “An algorithm producing a standard spine of a 3-manifold presented by surgery along a link”, Rend Circ Mat Palermo, 51:1 (2002), 179  crossref  mathscinet  zmath
    12. Stéphane Baseilhac, Riccardo Benedetti, “Quantum hyperbolic invariants of 3-manifolds with -characters”, Topology, 43:6 (2004), 1373  crossref
    13. Gennaro Amendola, “A calculus for ideal triangulations of three-manifolds with embedded arcs”, Math Nachr, 278:9 (2005), 975  crossref  mathscinet  zmath  isi
    14. Francesco Costantino, “A calculus for branched spines of 3-manifolds”, Math Z, 251:2 (2005), 427  crossref  mathscinet  zmath  isi
    15. S. S. Anisov, “Lower bounds for transversal complexity of torus bundles over the circle”, Mosc. Math. J., 6:1 (2006), 5–41  mathnet  crossref  mathscinet  zmath
    16. Simon A. King, “Ideal Turaev–Viro invariants”, Topology and its Applications, 154:6 (2007), 1141  crossref
    17. CHARLES FROHMAN, JOANNA KANIA-BARTOSZYNSKA, “THE QUANTUM CONTENT OF THE NORMAL SURFACES IN A THREE-MANIFOLD”, J. Knot Theory Ramifications, 17:08 (2008), 1005  crossref
    18. S. V. Matveev, “Virtual $3$-manifolds”, Sib. elektron. matem. izv., 6 (2009), 518–521  mathnet  mathscinet
    19. Ekaterina Pervova, “Generalized Mom-structures and ideal triangulations of 3–manifolds with nonspherical boundary”, Algebr. Geom. Topol, 12:1 (2012), 235  crossref
    20. YUYA KODA, “LINKS AND SPINES”, J. Knot Theory Ramifications, 21:03 (2012), 1250027  crossref
    21. Paola Cristofori, Michele Mulazzani, “Compact 3-manifolds via 4-colored graphs”, RACSAM, 2015  crossref
    22. V. M. Buchstaber, V. A. Vassiliev, A. Yu. Vesnin, I. A. Dynnikov, Yu. G. Reshetnyak, A. B. Sossinsky, I. A. Taimanov, V. G. Turaev, A. T. Fomenko, E. A. Fominykh, A. V. Chernavsky, “Sergei Vladimirovich Matveev (on his 70th birthday)”, Russian Math. Surveys, 73:4 (2018), 737–746  mathnet  crossref  crossref  adsnasa  isi  elib
    23. A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “New aspects of complexity theory for 3-manifolds”, Russian Math. Surveys, 73:4 (2018), 615–660  mathnet  crossref  crossref  adsnasa  isi  elib
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