## Lecture Notes in Mathematics, Volume 165 |

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Page 167

then the action of T here is to map D' to 0 and tjD' isomorphically onto D' . Look

back at Figure 2. Notice that ' and t^a ' are 4 unbounded. Thus they must have

then, ...

then the action of T here is to map D' to 0 and tjD' isomorphically onto D' . Look

back at Figure 2. Notice that ' and t^a ' are 4 unbounded. Thus they must have

**non**-**zero**boundaries: 0 ^ d (§^a') , 5 2 0 ji d (t^a'). From thederivation propertythen, ...

Page 168

The next

order to cancel, then, we must have d ( gja) A 0 > l2 3 d ( g^) ^ 0 . Let these new

elements be B^ € nl0^— 3^ ' Bl ^ nll^— 3^ . One reallv needs to check that B^ 6 ...

The next

**non**-**zero**elements remaining are as in Figure 3: ll l2 3 0 Figure 3 8 2 Inorder to cancel, then, we must have d ( gja) A 0 > l2 3 d ( g^) ^ 0 . Let these new

elements be B^ € nl0^— 3^ ' Bl ^ nll^— 3^ . One reallv needs to check that B^ 6 ...

Page 170

The next

25 26 Figure 5 Clearly dl2(§J) = dl2((^)2) = 2^ • dl2( ?*) = 2?|b' . Then we get it 2

2 addition B a and B'B a

The next

**non**-**zero**terms to appear * 1 11 are these: 2l 20 ll ?lBiBl ?iB l l Tl 23 2425 26 Figure 5 Clearly dl2(§J) = dl2((^)2) = 2^ • dl2( ?*) = 2?|b' . Then we get it 2

2 addition B a and B'B a

**non**-**zero**. So (A - D)B and 111 1 2 2 (A# - D)B|B^a ...### What people are saying - Write a review

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### Contents

Preliminaries LlBRARY | 1 |

EilenbergMacLane spaces and spectra | 31 |

SpanierWhitehead duality | 52 |

Copyright | |

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### Common terms and phrases

abelian category abelian groups algebra Assume basepoint bouquet of spheres cancellation cofibration cohomology commutative diagram composite congruence convergent spectrum Corollary CW space define degree diagram commutes dual duality element epimorphism exists fact fibration finite CW complex finite type Freyd functor given H X,A H X/A hence Hom(H homeomorphism homology theory homotopy groups idempotent implies indecomposable induces injective integer isomorphism ker cp Let f Let G long exact sequence map f mapping cone monomorphism morphism n-connected n-l)-connected n-spheres n+l n+l n+l natural transformation non-unit non-zero observe p-torsion primes Proof prove R-module ring Schanuel's Lemma Seiten Seminar Serre Serre Spectral Sequence Sn+l Spanier spherical retracts stable homotopy strongly convergent summand theories of bidegree topology trivial weak homotopy equivalence wedge of spheres Y V B yields