By Francesco Costantino
We determine a calculus for branched spines of 3-manifolds via branched Matveev-Piergallini strikes and branched bubble-moves. We in brief point out a few of its attainable functions within the research and definition of State-Sum Quantum Invariants.
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Extra resources for A calculus for branched spines of 3-manifolds
2. Now assume given a prime p and an idempotent functor Ep as in (c). 3, the standard map p~ : S 1 --* S 1 of degree n is an Ev-equivalence if (n,p) = 1, and thus, for every space X, the map (pn)*: IS ~, EpX] ~ [S 1, EpX] is a bijection. This tells us that ~r~(EpX) is a p-local group and hence separable. If we assume that (b) holds, then in particular ~: X ---* EvX is nuUhomotopic, and the universal property of 77forces EpX to be contractible. This shows that ( b ) ~ ( c ) . The implication ( c ) ~ ( d ) is trivial.
This situation is typical as shown by the main result in . 34 References 1. I. BOKOR, On Genus and Cancellation in Homotopy, Israel Journal of Mathematics 2. I. LLERENA,Wedge Cancellation of Certain Mapping Cones, Composi$io Mathe- (in press). matica (to appear). I. Bokor: Mathematik Berninaplatz 3 CH-8057 - Zfirieh Switzerland I. Llerena: Departament d'Algebra i Geometria Universitat de Barcelona Gran Via de les Corts Catalanes, 585 E-08007 Barcelona Spain 1990 Barcelona Conference on Algebraic Topology.
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