Geodesic
Transformations of special spines and the Zeeman conjecture
Izvestiya. Mathematics , Tome 31 (1988) no. 2, pp. 423-434.

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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. 
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S. V. Matveev. Transformations of special spines and the Zeeman conjecture. Izvestiya. Mathematics , Tome 31 (1988) no. 2, pp. 423-434. http://geodesic.mathdoc.fr/item/IM2_1988_31_2_a8/

[1] Zeeman E. C., Seminar on combinatorial topology, Inst. Hautes Etudes. Sci., Paris, 1963

[2] Casler B. G., “An embedding theorem for connected 3-manifolds with boundary”, Proc. Amer. Math. Soc., 16 (1965), 559–566 | DOI | MR | Zbl

[3] Matveev S. V., “Spetsialnye ostovy kusochno lineinykh mnogoobrazii”, Matem. sb., 92:2 (1973), 282–293 | MR | Zbl

[4] Matveev S. V., Savvateev V. V., “Trekhmernye mnogoobraziya, imeyuschie prostye spetsialnye ostovy”, Colloquium Mathematicum, XXXII:1 (1974), 83–97

[5] Ikeda H., “Finding simpler spines for acyclic 3-manifolds”, Math. Semin. Notes Kobe Univ., 10:1 (1982), 57–68 | MR | Zbl

[6] Gillman D., Rolfsen D., “The Zeeman conjecture for standard spines is equivalent to the Poincare conjecture”, Topology, 22:3 (1983), 315–323 | DOI | MR | Zbl