We provide a local calculus for the presentation of closed –manifolds via nullhomotopic filling Dehn spheres. We use it to define an invariant of closed –manifolds by applying the state-sum machinery, and we show how to potentially get lower bounds for the Matveev complexity of –irreducible closed –manifolds. We also describe an efficient and simple algorithm for constructing a nullhomotopic filling Dehn sphere of each closed –manifold from any of its one-vertex triangulations.
"A local calculus for nullhomotopic filling Dehn spheres." Algebr. Geom. Topol. 9 (2) 903 - 933, 2009. https://doi.org/10.2140/agt.2009.9.903