This book provides an introduction to the beautiful and deep
subject of filling Dehn surfaces in the study of topological
3-manifolds. This book presents, for the first time in English and
with all the details, the results from the PhD thesis of the first
author, together with some more recent results in the subject. It
also presents some key ideas on how these techniques could be used
on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces
is mostly self-contained requiring only basic knowledge on topology
and homotopy theory. The complete and detailed proofs are
illustrated with a set of more than 600 spectacular pictures, in
the tradition of low-dimensional topology books. It is a basic
reference for researchers in the area, but it can also be used as
an advanced textbook for graduate students or even for adventurous
undergraduates in mathematics. The book uses topological and
combinatorial tools developed throughout the twentieth century
making the volume a trip along the history of low-dimensional
topology.
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