COMBINATORIAL SUSPENSION FOR DISC HOMEOMORPHISMS

For a punctured disc homeomorphism given combinatorially, we give an a lgorithmic construction of the suspension flow in the corresponding ma pping-torus M-3. In particular, one computes explicitly the embedding in the S-manifold M-3 of any finite collection of periodic orbits for this flow. All these orbits are realized as closed braids carried by a branched surface (or template), which we construct in the algorithm. Our construction gives a combinatorial proof of the fact that the peri odic orbits of such a suspension flow are carried by a same branched s urface.