By J. P. May
This quantity introduces equivariant homotopy, homology, and cohomology idea, besides quite a few comparable issues in smooth algebraic topology. It explains the most principles in the back of the most outstanding contemporary advances within the topic. The e-book starts with a improvement of the equivariant algebraic topology of areas culminating in a dialogue of the Sullivan conjecture that emphasizes its courting with classical Smith idea. It then introduces equivariant strong homotopy concept, the equivariant good homotopy class, and an important examples of equivariant cohomology theories. the elemental equipment that's had to make severe use of equivariant solid homotopy idea is gifted subsequent, besides discussions of the Segal conjecture and generalized Tate cohomology. ultimately, the e-book offers an creation to ``brave new algebra", the research of point-set point algebraic constructions on spectra and its equivariant functions. Emphasis is put on equivariant complicated cobordism, and similar effects on that subject are provided intimately. good points: Introduces the various basic principles and ideas of recent algebraic topology. offers entire fabric now not present in the other e-book at the topic. presents a coherent review of many components of present curiosity in algebraic topology. Surveys loads of fabric, explaining major rules with out getting slowed down in information.