By F. R. Cohen (auth.), Haynes R. Miller, Douglas C. Ravenel (eds.)

ISBN-10: 3540184813

ISBN-13: 9783540184812

ISBN-10: 3540479864

ISBN-13: 9783540479864

During the wintry weather and spring of 1985 a Workshop in Algebraic Topology used to be held on the college of Washington. The direction notes through Emmanuel Dror Farjoun and through Frederick R. Cohen contained during this quantity are rigorously written graduate point expositions of yes points of equivariant homotopy concept and classical homotopy thought, respectively. M.E. Mahowald has integrated a number of the fabric from his extra papers, symbolize quite a lot of modern homotopy conception: the Kervaire invariant, reliable splitting theorems, desktop calculation of volatile homotopy teams, and stories of L(n), Im J, and the symmetric groups.

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**Extra resources for Algebraic Topology: Proceedings of a Workshop held at the University of Washington, Seattle, 1985**

**Sample text**

2. Let X denote the 6-skeleton of ~2S5. We shall check that the composite X inclusion ~2S5 f ~S3 has order 4 in [X,~S 3] where f is an H-map which is onto ~3" We claim that X is the cofibre of the composite S6 pinch S6vS6 3~'v[2]; S3vS6 where ~' is a generator for ~6S3[TI ] • 54 To prove this, f i r s t notice that ~S4 splits as S3×~S7 forcing the class in H6(~2S5) to be spherical. By inspection of the Serre exact sequence, X is the cofibre of some map g: S6 ÷ S3vS6. ~6(S3vS 6) is isomorphic to ~6S3~6 s6, by (k~')v[2] for some integer k.

7. That pn annihilates the p-primary component of x,S 2n+l, p odd, is proven in [CMN2] and [N3] using apparently different techniques. We shall try to find 2 primary analogues of Selick's retract theorem rather than pursuing odd primary information. 1. Let p be an odd prime and l e t f: ~p2p+2(p) ÷ S3 be any map which is onto ~2p" Then f , is a s p l i t epimorphism on the p-primary component of ~qS3, q>3. This theorem can be thought of as an analogue of the Kahn-Priddy theorem for S3. 4. Thus ~2S3<3> is a p-local retract of ~3p2p+2(p).

Since Kn is of f i n i t e type, i t suffices to prove that f is a monomorphism when r e s t r i c t e d to the module of primitives PKn. 1. ~3sn. following holds in any fixed degree: Furthermore, exactly one of the ( i ) PK is of dimension at most one n with basis (a) ,~a~b ~2j £~lq2Xn_3 ) , j>O, a>l, b>_O. 4: , a,j>_O. Let f: K2n+l ÷ K2n+l.

### Algebraic Topology: Proceedings of a Workshop held at the University of Washington, Seattle, 1985 by F. R. Cohen (auth.), Haynes R. Miller, Douglas C. Ravenel (eds.)

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