We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the 1980s by S. Lins for closed 3-manifolds, which is in turn dual to the earlier construction introduced by Pezzana’s school in Modena. In this context we establish some results concerning fundamental groups, connected sums, moves between graphs representing the same manifold, Heegaard genus and complexity, as well as an enumeration and classification of compact 3-manifolds representable by graphs with few vertices (≤ 6 in the non-orientable case and ≤ 8 in the orientable one).

Cristofori, P., Mulazzani, M. (2016). Compact 3-manifolds via 4-colored graphs. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS, 110(2), 395-416 [10.1007/s13398-015-0240-8].

Compact 3-manifolds via 4-colored graphs

MULAZZANI, MICHELE
2016

Abstract

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the 1980s by S. Lins for closed 3-manifolds, which is in turn dual to the earlier construction introduced by Pezzana’s school in Modena. In this context we establish some results concerning fundamental groups, connected sums, moves between graphs representing the same manifold, Heegaard genus and complexity, as well as an enumeration and classification of compact 3-manifolds representable by graphs with few vertices (≤ 6 in the non-orientable case and ≤ 8 in the orientable one).
2016
Cristofori, P., Mulazzani, M. (2016). Compact 3-manifolds via 4-colored graphs. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS, 110(2), 395-416 [10.1007/s13398-015-0240-8].
Cristofori, Paola; Mulazzani, Michele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/599589
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