Invariants of Closed 3-Manifolds via Nullhomotopic Filling Dehn Spheres

Abstract

We provide a calculus for the presentation of closed 3-manifolds via nullhomotopic filling Dehn spheres and we use it to define an invariant of closed 3-manifolds by applying the state-sum machinery. As a potential application of this invariant, we show how to get lower bounds for the Matveev complexity of P2-irreducible closed 3-manifolds. We also describe an easy algorithm for constructing a nullhomotopic filling Dehn sphere of each closed 3-manifold from any of its one-vertex triangulations.

33 pages, 38 figures; added two open questions in Section 3; corrected Figure 11

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