We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on 2-irreducible manifolds. Moreover, for 2-irreducible manifolds, it equals the minimal number of cubes in a cubulation of the manifold, except for the sphere S3, the projective space 3 and the lens space L4,1, which have surface-complexity zero. We will also give estimations of the surface-complexity by means of triangulations, Heegaard splittings, surgery presentations and Matveev complexity. © 2010 World Scientific Publishing Company.

Amendola, G. (2010). A 3-manifold complexity via immersed surfaces. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 19(12), 1549-1569 [10.1142/S0218216510008558].

A 3-manifold complexity via immersed surfaces

AMENDOLA, GENNARO
2010

Abstract

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on 2-irreducible manifolds. Moreover, for 2-irreducible manifolds, it equals the minimal number of cubes in a cubulation of the manifold, except for the sphere S3, the projective space 3 and the lens space L4,1, which have surface-complexity zero. We will also give estimations of the surface-complexity by means of triangulations, Heegaard splittings, surgery presentations and Matveev complexity. © 2010 World Scientific Publishing Company.
No
Articolo in rivista - Articolo scientifico
Scientifica
3-manifold, complexity, immersed surface, cubulation
English
Amendola, G. (2010). A 3-manifold complexity via immersed surfaces. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 19(12), 1549-1569 [10.1142/S0218216510008558].
Amendola, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/8649
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