Eqüivariant Cohomology Theories
نویسنده
چکیده
Throughout this note G denotes a discrete group. A G-complex is a CPP-complex on which G acts by cellular maps such that the fixed point set of any element of G is a subcomplex. On the category of pairs of G-complexes and equivariant homotopy classes of maps, an equivariant cohomology theory is a sequence of contravariant functors 3C into the category of abelian groups together with natural transformations 8: 3C(L, 0)—»3C(i£, L) such that (1) W»(KSJL, L) ~>3C(K, KC\L) induced by inclusion, (2) • • • ->3C(K, L)~^JC(i^)~»JC(L)-~>5C(^ £ ) * • • • is exact. (3) If S is a discrete G-set with orbits Sa then I l £ : 3C"(5)->Il3C(^) a a
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