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 was once held on the college of Washington. The direction notes by way of Emmanuel Dror Farjoun and through Frederick R. Cohen contained during this quantity are rigorously written graduate point expositions of convinced facets of equivariant homotopy conception and classical homotopy idea, respectively. M.E. Mahowald has integrated a number of the fabric from his extra papers, characterize a variety of modern homotopy idea: the Kervaire invariant, sturdy splitting theorems, machine calculation of volatile homotopy teams, and reports of L(n), Im J, and the symmetric groups.

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**Example text**

5 and show that pRh is null. Hence there is a map h: ~2S3 ÷ map,(p3(p),S 2p+I P l i f t i n g ~hp. 2. Notice that a choice of generator for H2p_I~2S3 suspends to the p-th power in H2p~S3. Thus (ghp), is onto H2p_l. Since H2p_2(map,(p3(p),s2p+I);~) i s ~ / p by the Hurewicz theorem, i t follows that h, is an isomorphism on H2p_2 by commutation with the homology Bockstein. Thus to construct h, i t suffices to prove the following lemma. 5. Proof: ~hp has order p in [~2s2n+l,~2S2np+l]. There is a commutative diagram ~S2n+l _ _hp, ~[p]~ ~S2np+1 ~ a[p p] ~S2n+l .....

D(f) is null. Hence D(f) l i f t s to Fl by a map D(f). This l i f t is not unique. Inductively, define Fq+l to be the fibre of the inclusion FqVFq+ FqXFq and Dq+l(f)=D(Dq(f)). Inductively define ~q+l: Fq+l ÷ X by setting ~q+l V~ equal to the composite Fq+l ÷ FqVFq q q> X where ~l is the composite Fl ÷ z2Bvs2B ~W> X. Notice that ~q+l has order 2 because it is given in terms of iterated Whitehead products. By definition ~s+l'Ds+l(f)=(2~s)'Ds(f)-2(~s'Ds(f)). If Hi{Z2A)=O for i~n2q-I and z2B is n-connected, then Dq(f) is null and thus 2q(~f)=O.

2a~a-I 2 -0, ~ 2a-l~a-I But ~q. Q3Yn_3bq. ~I Q3Yn_3=o because 2i^a-I SqIQ3Yn_3=O and ~q. ql Q3Yn_3=O i f i

### 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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