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This article is cited in 2 scientific papers (total in 2 papers)
New aspects of complexity theory for 3-manifolds
A. Yu. Vesninab, S. V. Matveevcd, E. A. Fominykhcd a Tomsk State University
b S. L. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
c Chelyabinsk State University
d N. N. Krasovskii Institute of Mathematics and Mechanics of Russian Academy of Sciences
Abstract:
Recent developments in the theory of complexity for three-dimensional manifolds are reviewed, including results and methods that emerged over the last decade. Infinite families of closed orientable manifolds and hyperbolic manifolds with totally geodesic boundary are presented, and the exact values of the Matveev complexity are given for them. New methods for computing complexity are described, based on calculation of the Turaev–Viro invariants and hyperbolic volumes of 3-manifolds.
Bibliography: 89 titles.
Keywords:
3-manifolds, Matveev complexity, tetrahedral complexity, triangulations, spines.
Received: 09.04.2018
Citation:
A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “New aspects of complexity theory for 3-manifolds”, Uspekhi Mat. Nauk, 73:4(442) (2018), 53–102; Russian Math. Surveys, 73:4 (2018), 615–660
Linking options:
https://www.mathnet.ru/eng/rm9829https://doi.org/10.1070/RM9829 https://www.mathnet.ru/eng/rm/v73/i4/p53
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Abstract page: | 695 | Russian version PDF: | 128 | English version PDF: | 30 | References: | 74 | First page: | 57 |
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