Introduction
This volum e bega n wit h Bo b Piacenza' s suggestio n tha t I b e th e principa l lec -
turer a t a n NSF/CBM S Regiona l Conferenc e whic h h e would organiz e i n Fair -
banks, Alaska . Th e conferenc e too k plac e i n August , 1993, an d I sen t hi m a
draft o f the boo k earl y i n January , 1995. H e sen t m e a n e-mai l o n Januar y 15,
1995, sayin g
"Peter, Bes t new s this holiday . Goo d Goo d Good! "
On Januar y 22 , 1995, he die d unexpectedl y an d peacefull y a t home . Thi s boo k
is dedicated t o his memory .
The period since the conference ha s seen very substantial progress in this gen-
eral are a o f mathematics. Th e scop e o f this volum e ha s grow n accordingly . It s
original focu s wa s a n introductio n t o equivarian t algebrai c topology , t o stabl e
homotopy theory , an d t o equivarian t stabl e homotop y theor y tha t wa s geare d
towards graduat e student s wit h a reasonabl y goo d understandin g o f nonequiv -
ariant algebrai c topology . Mor e recent materia l i s changing th e directio n o f th e
last tw o subject s b y allowin g th e introductio n o f point-se t topologica l algebr a
into stable homotopy theory, both equivariant an d non-equivariant, an d th e las t
portion of the book focuses on an introduction to these new developments. Ther e
is a progression , wit h th e late r portion s o f th e boo k o n th e whol e bein g mor e
difficult tha n th e earlie r portions .
Equivariant algebrai c topolog y concern s th e stud y o f algebrai c invariant s o f
spaces with grou p actions . Th e firs t tw o chapters introduc e th e basic structura l
foundations o f th e subject : cellula r theory , ordinar y homolog y an d cohomol -
ogy theory , Eilenberg-Ma c Lane G-spaces , Postniko v systems , localization s o f
G-spaces and completions o f G-spaces. I n most o f this work, G can be an y topo-
logical group , bu t w e restrict attentio n t o compac t Li e groups in the res t o f th e
book.
Chapter III , on equivariant rational homotopy theory, was written by Georgi a
Triantafillou. I n it , sh e show s ho w t o generaliz e Sullivan' s theor y o f minima l
models to obtai n a n algebraizatio n o f th e homotop y categor y o f (nilpotent ) G -
spaces for a finit e grou p G. Thi s chapte r contain s a first surprise : rationa l Hop f
G-spaces nee d no t spli t a s product s o f Eilenberg-Ma c Lane G-spaces . Thi s i s
l
http://dx.doi.org/10.1090/cbms/091/01
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