A LOWER BOUND FOR THE GENUS OF SELF-AMALGAMATION OF HEEGAARD SPLITTINGS

Abstract

Let M be a compact orientable closed 3-manifold, and F a non-separating incompressible closed surface in M. Let M' = M - <TEX>${\eta}(F)$</TEX>, where <TEX>${\eta}(F)$</TEX> is an open regular neighborhood of F in M. In the paper, we give a lower bound of genus of self-amalgamation of minimal Heegaard splitting <TEX>$V'\;{\cup}_{S'}\;W'$</TEX> of M' under some conditions on the distance of the Heegaard splitting.