A 3-MANIFOLD COMPLEXITY VIA IMMERSED SURFACES

作者：Amendola Gennaro^*

来源：Journal of Knot Theory and Its Ramifications, 2010, 19(12): 1549-1569.

DOI：10.1142/S0218216510008558

• 3-manifold
• complexity
• immersed surface
• cubulation

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 P-2-irreducible manifolds. Moreover, for P-2-irreducible manifolds, it equals the minimal number of cubes in a cubulation of the manifold, except for the sphere S-3, the projective space RP3 and the lens space L-4,L-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.

• 出版日期2010-12