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 P²-irreducible manifolds. Moreover, for P²-irreducible manifolds, it equals the minimal number of cubes in a cubulation of the manifold, except for the sphere S³, the projective space RP³ and the lens space L₄₁, 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.
|Citazione:||Amendola, G. (2010). A 3-manifold complexity via immersed surfaces. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2010.|
|Tipo:||Articolo in rivista - Articolo scientifico|
|Carattere della pubblicazione:||Scientifica|
|Titolo:||A 3-manifold complexity via immersed surfaces|
|Data di pubblicazione:||2010|
|Rivista:||JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS|
|Appare nelle tipologie:||01 - Articolo su rivista|