ABSTRACT

Equivariant stable homotopy theory considers spaces and spectra endowed with the action of a fixed group G. There are many wonderful references for much of the foundational material in equivariant stable homotopy theory. The Cartesian product and function spaces with conjugation action give a closed symmetric monoidal structure on TopG. There are several different conceptual approaches to stabilization in G-spectra, and somewhat surprisingly, these lead to the same results. There are two dominant themes: one geometric and one algebraic. Boardman’s stable homotopy category was defined as an extension of the ordinary Spanier–Whitehead category under colimits. Many of the standard arguments apply without change here. The equivariant Spanier–Whitehead category is additive: finite wedges and products exist and agree and the morphism sets are naturally abelian group valued. The composition and symmetric monoidal products induce bilinear maps on morphism sets.