Preface xv
light editing before posting each installation for the students. Thus,
the students had the text growing in front of their eyes in real time.
By the end of the Fall semester the notes were complete: addi-
tional work involved further editing and, in a few cases, completing
and expanding proofs; a slight reordering of material to make each
chapter consist of complete lectures; and in a couple of cases, merging
two lectures into one, if in class a considerable repetition appeared.
But otherwise the book fully retained the structure of the original one-
semester course, and its expansion is due to the addition of a large
number of pictures, a number of exercises (some were originally given
in separate homework sets, others added later), and some “prose”,
i.e. discussions and informal explanations. All results presented in
the book appeared in the course, and, as I said before, only in a few
cases did proofs need to be polished or completed.
Aside from creating the original notes, my co-author Vaughn Cli-
menhaga participated on equal terms in the editorial process, and,
very importantly, he produced practically all of the pictures, includ-
ing dozens of beautiful 3-dimensional images for which, in many cases,
even the concept was solely his. Without him, I am absolutely sure
that I would not have been able to turn my course into a book in
anything approaching the present timeframe, and even if I did at all,
the quality of the final product would have been considerably lower.
Anatole Katok
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