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Geometry and Applications
March 13-16, 2000
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University
Novosibirsk, Russia

Organizers
Yu.G. Rushetnyak (Chair of Program Committee; Russia), V.V. Vershinin (Chair of Organizing Committee; Russia), A.A. Borisenko (Ukraine), Yu.D. Burago (Russia), V.M. Gol'dshtein (Israel), M.L. Gromov (France), I.G. Nikolaev (USA/Russia), S.P. Novikov (USA/Russia), A.V. Pogorelov (Ukraine), I.Kh. Sabitov (Russia)

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On order one transformations of manifolds triangulations
by
Artem Macovetsky
Chelyabinsk State University

It is known [A] that any two triangulations of the same manifold have common star subdivision. The sequence of transformations from given triangulation to common star subdivision consist of transformations that increase number of vertices in triangulation. Also, any transformation of order k is the resultant of transformations of order one.

Theorem. Let T1 and T2 be triangulations of a manifold M. Then there is trangulation T3 of M, such that one can pass from T1 to T3 and from T2 to T3 by increasing transformations of order one only.

This work is partially supported by the RFBR grant N 99-01-00813, and by INTAS, grant N 97-0808.

References.

[A] J. Alexander. The combinatorial theory of complexes. Annals of Math. (2), 31(1930), P.294-322.

Date received: February 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadw-31.