XVI
Preface
ABRAHAM-MARSDEN [AM], AEBISCHER et al. [Ae], GUILLEMIN-STERN-
BERG [GS], HOFER-ZEHNDER [HZ], MCDUFF-SALAMON [MS], SIEGEL
[Sil],
SOURIAU
[So],
VAISMAN
[V],
WALLACH
[W] and
WOODHOUSE
[Wo].
Instead we have tried to introduce the reader to the material in these sources
and, moreover, to follow the work contained in, for example,
GROMOV
[Gr]
and KiRlLLOV [Ki]. In the hope that this will provide each reader with a
starting point into this fascinating area a few parts of chapters 1,2, and 4
may be skipped by those whose interests lie in physics, and one may begin
directly with the sections on Hamiltonian vectorfields, moment maps and
quantization.
This text is, with minor changes, a translation of the book "Einfuhrung
in die Symplektische Geometrie" (Vieweg, 1998). The production of this text
has only been possible through the help of many. U. Schmickler-Hirzebruch
and G. Fischer, on the staff of Vieweg-Verlag, have made many valuable
suggestions, as has E. Dunne from the American Mathematical Society.
My colleagues J. Michalicek, O. Riemenschneider and P. Slodowy, from the
Mathematische Seminar of the Universitat Hamburg, were always, as ever,
willing to discuss these topics. A. Glinther prepared one draft of this text,
and I. Kowing did a newer draft and also showed great patience for my eter-
nal desire to have something or other changed. I also had very successful
technical consultation with F. Berndt, D. Nitschke and R. Schmidt. The last
of these went through the German text with great attention and smoothed
out at least some of what was rough in the text. I would also thank T.
Wurzbacher, W. Foerg-Rob and P. Wagner for carefully reading (parts of)
the German text and finding some misprints, wrong signs and other mis-
takes. The translation was done by M. Klucznik, who had an enormous task
in producing very fluent English (at least in my opinion) and a fine layout
of my often rather involved German style. It is a great joy for me to thank
each of these.
R. Berndt
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