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 \ygraph s, \cite{Gu,Ha}. One surprise is that the upper bounds depend on a bit more than a choice of generators for $H_1$. 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 $H_1$.
Key words: Finite type invariants, Goussarov-Habiro, Y-graphs.
Notes: 10 pages.