Topology Proceedings 30 No. 1 (2006), pp. 403-416

Factoring Positive Braids Via Branched Manifolds

Michael C. Sullivan

We show that a positive braid is composite if and only if the factorization is "visually obvious" by placing the braid k in a specially constructed smooth branched 2-manifold B(k) and studying how a would-be cutting sphere meets B(k). This gives an elementary proof of a theorem due to Peter Cromwell [Positive braids are visually prime, Proc. London Math. Soc. (3) 67 (1993), 384-424].

Keywords: branched manifolds, factoring knots, knot theory, positive braids

Mathematics Subject Classification: 57M25

Document formats: PDF file 160.6 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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