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 iciness and spring of 1985 a Workshop in Algebraic Topology was once held on the college of Washington. The path notes by way of Emmanuel Dror Farjoun and by way of Frederick R. Cohen contained during this quantity are conscientiously written graduate point expositions of definite points of equivariant homotopy concept and classical homotopy concept, respectively. M.E. Mahowald has integrated a number of the fabric from his additional papers, signify quite a lot of modern homotopy idea: the Kervaire invariant, strong splitting theorems, laptop calculation of volatile homotopy teams, and experiences of L(n), Im J, and the symmetric groups.

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

**Example text**

Also g~ is null because i t is the composition of two successive maps in a f i b r a t i o n . 5 and the lemma follows. 1. 57 §14. A f i l t r a t i o n of Q R P~ In this section we give a natural f i l t r a t i o n of Q~P~. The point of this is to consider the Kahn-Priddy theorem, one form of which states that the component of the base-point ~ oS ~ is a 2-1ocal retract of QtRP~[KP]. (A,X) denote the space of pointed maps from A to X. Let fn:~p2n + S4n be a fixed smooth embedding and write A2n+l=S4n-fn~Rp2n).

The diagonal is then given by the Cartan formula. Recall that QX=lim ~nznx. 3. I f X is path-connected, there is an isomorphism of algebras 7z/2[QlX] ÷ H,QX for admissible I and x runs over a basis for H,X. then the elements QIx are primitive. I f X is a suspension, The Steenrod operations are given by the Nishida relations st,qrXq = z(t-2i,r+q-2t+2i)er_t+2iS~,Xq i We will also have occasion to use the mod-p homology of ~2S3 for p odd and state the requisite result here. 4. Let p denote an odd prime.

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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