Abstract
For three-dimensional manifolds with the structure of a combinatorial block complex, we construct an invariant that allows one to verify the existence of isomorphisms, between these manifolds. For complexes of small dimensionality, we solve the problem on the possibility of extending the isomorphisms of subcomplexes to those of complexes.
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References
K. Reidemeister,Einführung in die kombinatorische Topologie, Vieweg (1932).
A. J. Sieradski, “Combinatorial squashings, 3-manifolds, and the third homology of groups,”Invent. Math.,84, 121–139 (1986).
H. Zieshang, “On Heegaard diagrams of 3-manifolds,”Asteisque,163/164, 247–280 (1988).
S. V. Matveev and A. T. Fomenko,Algorithmic and Computer Methods in Three-Dimensional Topology [in Russian], Moscow University, Moscow (1991).
A. O. Prishlyak, “Graphs imbedded into surfaces,”Usp. Mat. Nauk,52, Issue 4, 211–212 (1997).
Additional information
Shevchenko National University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal., Vol. 51, No. 4, pp. 568–571, April, 1999.
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Prishlyak, A.O. Isomorphisms of combinatorial block decompositions of three-dimensional manifolds. Ukr Math J 51, 636–638 (1999). https://doi.org/10.1007/BF02591766
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DOI: https://doi.org/10.1007/BF02591766