Volume 9, issue 2 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R42
References
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/