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Tabulation of three-dimensional manifolds. (English) Zbl 1137.57023

Russ. Math. Surv. 60, No. 4, 673-698 (2005); translation from Usp. Mat. Nauk 60, No. 4, 97-122 (2005).
Summary: The formation of tables of three-dimensional manifolds requires the development and computer realization of two algorithms: the listing algorithm and the recognition algorithm. In this paper the theoretical foundations of these algorithms are presented and a survey of results concerning the practical tabulation of three-dimensional manifolds is given.

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M15 Relations of low-dimensional topology with graph theory
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57-04 Software, source code, etc. for problems pertaining to manifolds and cell complexes
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