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A finite graphic calculus for 3-manifolds. (English) Zbl 0856.57009

The authors study “standard spines” of 3-manifolds. They obtain necessary and sufficient conditions for a “standard polyhedron” to be a standard spine of an orientable 3-manifold. They find a way to describe compact oriented 3-manifolds by planar graphs with some additional structure. They call these decorated graphs. The decorated graph corresponds to a standard spine with additional structure. They call these decorated spines. They go on to describe a calculus on the graphs which follows from Matveev-Piergallini moves on standard spines, these being described for example in [R. Piergallini, Standard moves for standard polyhedra and spines, Topology, 3rd Natl. Meet., Trieste/Italy 1986, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 18, 391-414 (1988; Zbl 0672.57004)].

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M15 Relations of low-dimensional topology with graph theory

Citations:

Zbl 0672.57004
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References:

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