  Foams are surfaces with branch lines at which three sheets merge. They have
been used in the categorification of sl(3) quantum knot invariants and also in
physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of
commutative Frobenius algebras, where saddle points correspond to
multiplication and comultiplication. In this paper, we explore algebraic
operations that branch lines derive under TQFT. In particular, we investigate
Lie bracket and bialgebra structures. Relations to the original Frobenius
algebra structures are discussed both algebraically and diagrammatically.
