Equivariant homotopy theory started from geometrically motivated
questions about symmetries of manifolds. Several important
equivariant phenomena occur not just for a particular group, but in
a uniform way for all groups. Prominent examples include stable
homotopy, K-theory or bordism. Global equivariant homotopy theory
studies such uniform phenomena, i.e. universal symmetries encoded
by simultaneous and compatible actions of all compact Lie groups.
This book introduces graduate students and researchers to global
equivariant homotopy theory. The framework is based on the new
notion of global equivalences for orthogonal spectra, a much finer
notion of equivalence than is traditionally considered. The
treatment is largely self-contained and contains many examples,
making it suitable as a textbook for an advanced graduate class. At
the same time, the book is a comprehensive research monograph with
detailed calculations that reveal the intrinsic beauty of global
equivariant phenomena.
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