The mystery of the brane relation
Stavros Garoufalidis
Abstract
The purpose of the present paper is to introduce and explore two surprises that arise when we apply a standard procedure to study the number of finite type invariants of 3-manifolds introduced independently by M. Goussarov and K. Habiro based on surgery on claspers, Y-graphs or clovers, Gu,Ha,GGP. One surprise is that the upper bounds depend on a bit more than a choice of generators for H1. A complementary surprise a curious brane relation (in two flavors, open and closed) which shows that the upper bounds are in a certain sense independent of the choice of generators of H1.
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