  We propose a generalization of the classical notions of plumbing and Murasugi
summing operations to smooth manifolds of arbitrary dimensions, so that in this
general context Gabai's credo "the Murasugi sum is a natural geometric
operation" holds. In particular, we prove that the sum of the pages of two open
books is again a page of an open book and that there is an associated summing
operation of Morse maps. We conclude with several open questions relating this
work with singularity theory or contact topology.

Geometric Topology;Symplectic Geometry