Behavior of the extended complexity of irreducible 3-manifolds

O. N. Shatnykh

Kurgan State University

Abstract: We construct the extended complexity of irreducible 3-manifolds; unlike the usual complexity [1] it is not an integer, but an ordered tuple of five integers. The benefit of extended complexity is that it always decreases when a manifold is cut along some incompressible boundary incompressible surface.

Keywords: 3-manifold, spine, complexity.

UDC: 515.16

Received: 28.06.2007

 English version: Siberian Mathematical Journal, 2008, 49:3, 562–568

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