  We present a topological construction that provides many examples of
non-commutative Frobenius algebras that generalizes the well-known
pair-of-pants. When applied to the solid torus, in conjunction with
Crane-Yetter theory, we provide a topological proof of the Verlinde formula. We
also apply the construction to a solid handlebody of higher genus, leading to a
generalization of the Verlinde formula (not the higher genus Verlinde formula);
in particular, we define a generalized $S$-matrix. Finally, we discuss the
relation between our construction and Yetter's construction of a handle as a
Hopf algebra, and give a generalization.
