#### Volume 9, issue 2 (2009)

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A local calculus for nullhomotopic filling Dehn spheres

### Gennaro Amendola

Algebraic & Geometric Topology 9 (2009) 903–933
##### Abstract

We provide a local calculus for the presentation of closed $3$–manifolds via nullhomotopic filling Dehn spheres. We use it to define an invariant of closed $3$–manifolds by applying the state-sum machinery, and we show how to potentially get lower bounds for the Matveev complexity of ${ℙ}^{2}$–irreducible closed $3$–manifolds. We also describe an efficient and simple algorithm for constructing a nullhomotopic filling Dehn sphere of each closed $3$–manifold from any of its one-vertex triangulations.

##### Keywords
3-manifold, immersed surface, local calculus, invariant, state sum, complexity
Primary: 57M27
Secondary: 57R42
##### Publication
Received: 29 January 2008
Revised: 31 October 2008
Accepted: 21 December 2008
Published: 5 May 2009
##### Authors
 Gennaro Amendola Department of Mathematics University of Salento Palazzo Fiorini Via per Arnesano I-73100 Lecce Italy http://www.dm.unipi.it/~amendola/