HEEGAARD GENERA OF ANNULAR 3-MANIFOLDS

Abstract

Let M be a compact orientable 3-manifold, and A an essential annulus which cuts M into two 3-manifolds M 1 and M 2 . We denote by g(M) the Heegaard genus of M. In this paper, we will give a lower bound to g(M) when M i contains no bounded essential surfaces with large Euler's characteristic, where all boundary components of the essential surfaces lie in A.