A calculus for branched spine of 3-manifolds

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We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.
15 pages, 12 figures. Revised version, to appear in Mathematische Zeitschrift

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