By Anthony Bak (auth.), R. Keith Dennis (eds.)

ISBN-10: 0387119663

ISBN-13: 9780387119663

ISBN-10: 3540119663

ISBN-13: 9783540119661

ISBN-10: 3540395563

ISBN-13: 9783540395560

**Read or Download Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part II PDF**

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**Additional info for Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part II**

**Sample text**

In equivariant homotopy in H. examples of the G-spaces introduced classes of based G-maps X + Y. 2 in section 3. let IX,Y] G denote the set In particular, for H C G, it is stan- 26 H(y) q = [(G/H)+ A sq,Y] G = [sq,Y H] = ~ (yH), q where S q is the q-sphere with trivial G-action. Here and henceforward, the union of a G-space X and a disjoint G-fixed basepoint. to be a weak G-equivalence have the homotopy consider, such an f is necessarily natural to consider A G-map f:X + Y is said if each fH:xH ÷ yH is a weak equivalence.

To B(G,GLA) × Z, and its irrelevance our theory. telescope By cofinality, B~(A,G) We illustrate maps. of copies of {W t} The resulting explains why B(G,GLA) by the noncofinal telescope is G-equivalent plays no explicit role in we do have a natural G-map from B(G,GLA) x Z to the defined as above the respect the force of Proposition Let f :B ÷ A be a ring homomorphism. to the sequence {Wt}. 2 by using it to construct Applying naturality f to matrix entries, we obtain homomorphisms f#:GL(n,B) + GL(n,A).

If f:X ÷ Y is a group completion and we form X and ~ with respect to a cofinal sequence in X and its image in Y, then f commutes up to G-homotopy with the translations and therefore factors up to G-homotopy as a composite X+~ ~ = Y. The construction commutes with passage to fixed point spaces, and it is a direct consequence of the group completion property that each on homology. ~H induces an isomorphism By an easy (but not obvious) homotopical argument, this implies the following universal property of f; see [8] for details.

### Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part II by Anthony Bak (auth.), R. Keith Dennis (eds.)

by George

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