This book is part of the series of three books arise from lectures
organized by Hitoshi Murakami at RIMS, Kyoto University in the
summer of 2001. The lecture series was aimed at a broad audience
that included many graduate students. Its purpose lay in
familiarizing the audience with the basics of 3-manifold theory and
introducing some topics of current research. The first portion of
the lecture series was devoted to standard topics in the theory of
3-manifolds. The middle portion was devoted to a brief study of
Heegaard splittings and generalized Heegaard splittings.In the
standard schematic diagram for generalized Heegaard splittings,
Heegaard splittings are stacked on top of each other in a linear
fashion. This can cause confusion in those cases in which
generalized Heegaard splittings possess interesting connectivity
properties. Fork complexes were invented in an effort to illuminate
some of the more subtle issues arising in the study of generalized
Heegaard splittings.
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