Contents
Introduction 1
Chapter I . Equivarian t cellula r an d homolog y theor y 11
1. Some basic definition s an d adjunction s 11
2. Analogues for base d G-space s 12
3. G-C W complexe s 13
4. Ordinary homolog y an d cohomolog y theorie s 16
5. Obstruction theor y 18
6. Universal coefficien t spectra l sequence s 19
Chapter II . Postniko v systems , localization , an d completio n 2 1
1. Eilenberg-MacLane G-space s an d Postniko v system s 2 1
2. Summary: localization s o f spaces 2 2
3. Localization s o f G-space s 2 3
4. Summary : completion s o f spaces 2 4
5. Completion s o f G-space s 2 6
Chapter III . Equivarian t rationa l homotop y theor y (b y Georgi a
Triantafillou) 2 7
1. Summary: th e theory o f minimal model s 2 7
2. Equivariant minima l models 2 9
3. Rationa l equivarian t Hop f space s 3 1
Chapter IV . Smit h theor y 3 3
1. Smith theor y via Bredon cohomolog y 3 3
2. Borel cohomology, localization , an d Smit h theory 3 5
Chapter V . Categorica l constructions ; equivarian t application s 3 9
1. Coends an d geometri c realization 3 9
2. Homotopy colimit s an d limit s 4
3. Elmendorf's theore m o n diagram s o f fixed poin t space s 4 3
4. Eilenberg-Mac Lane G-space s an d universa l ^-spaces 4 5
Chapter VI . Th e homotop y theor y o f diagram s (b y Rober t J .
Piacenza) 4 7
1. Elementary homotop y theor y o f diagrams 4 7
2. Homotopy group s 4 9
3. Cellula r theor y 5 0
4. The homolog y an d cohomolog y theor y o f diagrams 5 2
5. The close d model structur e o n
UJ
5 3
6. Another proo f o f Elmendorf's theore m 5 6
Chapter VII . Equivarian t bundl e theor y an d classifyin g space s 5 9
1. The definitio n o f equivariant bundle s 5 9
2. The classificatio n o f equivariant bundle s 6 0
3. Some examples o f classifying space s 6 2
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