# Download e-book for kindle: Algebraic K-Theory: Proceedings of a Conference Held at by Anthony Bak (auth.), R. Keith Dennis (eds.)

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

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

**Sample text**

Let k r be the field with r = qa elements, where q is a prime which does not divide the order of G. the G-maps Let ~r-I:K(G) + K(G) and F~r(G) and Four(G) be the homotopy fibres of ~r-I:KO(G) + KO(G). Then Brauer lifting induces G-homotopy equivalences B:K(kr,G) ÷ F~r(G) and ~ :KO(kr,G) ÷ Four(G). By the five lemma, this allows application of the reservoir of known information about KG(X) to the calculation of the functor [X,K(kr,G)]G, and similarly in the (technically deeper) orthogonal ease. It is a pleasure to thank Martin Isaacs, Irving Kaplansky, and David Leep for helpful conversations.

The central one algebraically, 4. invariants K-groups when Y = K(G) We write KGA = ~GK(A,G) q q in the orthogonal V of G. K-theory of G-bundles hence the homotopy groups above are all examples of (reduced) and similarly It is also the "homotopy groups" where Sv is the one-point equivariant If X and Y as holds for all G-spaces we shall a G-homotopy ~(Y) or Y = KO(G). X+ denotes give the equivariant the equivariant Q- version of Quillen's and prove the equivalence second of the two notions. This can all be done, and an exposition will appear in Benioff [5].

If char F # 2, 41 this implies that S = {VIv ~ v* and every b is skew symmetric If V ¢ S, and b is not s y ~ e t r i c , nondegenerate S then a(v,w) = b(v,w) - b(w,v) must be and is thus a skew symmetric G-form. If char F ~ 2, this gives = {V I V admits both symmetric and skew symmetric For an F[G]-module V, let hV = (V ~ V * , module. }. G'forms}. h) be the hyperbolic orthogonal F[G]- The G-form h is specified by h((v,f),(w,g)) Note that hV = hV*. prematurely = g(v) + f(w) for v,wE V and f,g~ V*.

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

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