A local calculus for nullhomotopic filling Dehn spheres

Amendola, Gennaro

doi:10.2140/agt.2009.9.903

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A local calculus for nullhomotopic filling Dehn spheres

Gennaro Amendola

Algebraic & Geometric Topology 9 (2009) 903–933

DOI: 10.2140/agt.2009.9.903

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

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/

Volume 9, issue 2 (2009)