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    We summarize the known obstructions to subfactors with principal graphs which begin with a triple point. One is based on Jones's quadratic tangles techniques, although we apply it in a novel way. The other two are based on connections techniques; one due to Ocneanu, and the other previously unpublished, although likely known to Haagerup.

    We then apply these obstructions to the classification of subfactors with index below 5. In particular, we eliminate three of the five families of possible principal graphs called "weeds" in the classification from S. Morrison and N. Snyder, Subfactors of index less than 5, part 1: the principal graph odometer, to appear in Comm. Math. Phys.

    This paper is available online at arXiv: 1007.2240, and at

    AMSC: 46L37, 18D10