By Martin Arkowitz, Gregory Lupton (auth.), Carles Broto, Carles Casacuberta, Guido Mislin (eds.)

ISBN-10: 3034890184

ISBN-13: 9783034890182

ISBN-10: 303489869X

ISBN-13: 9783034898690

Central to this number of papers are new advancements within the basic concept of localization of areas. This box has gone through great swap of past due and is yielding new perception into the mysteries of classical homotopy conception. the current quantity contains the refereed articles submitted on the convention on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. numerous finished articles on basic localization make clear the elemental instruments and provides a document at the state-of-the-art within the subject material. The textual content is hence obtainable not just to the pro mathematician but additionally to the complicated student.

**Read or Download Algebraic Topology: New Trends in Localization and Periodicity: Barcelona Conference on Algebraic Topology, Sant Feliu de Guíxols, Spain, June 1–7, 1994 PDF**

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**Extra resources for Algebraic Topology: New Trends in Localization and Periodicity: Barcelona Conference on Algebraic Topology, Sant Feliu de Guíxols, Spain, June 1–7, 1994**

**Example text**

Proof. 5. -local. K. 7. THE EQUIVALENT CATEGORIES M~Hos AND M~Hos. For n ~ 1, the nth chromatic layer of a spectrum E is now given by M~E = r n-1L~E, and the nth monochromatic homotopy category M~Hos consists of the [Wn,-k trivial [Wn- b -]*-colocal spectra. Similarly, we let M~E = n-1L~E and the homotopy category M~Hos consists of the [Wn, -]*-trivial Wn-h-Iocal spectra. These would be the K(n)*-local spectra if the telescope conjecture were valid. We may view M~ H OS and M~ H as as alternative forms of the nth stable monochromatic homotopy category since there are adjoint equivalences r r n'.

Thus W kills the GEM F, and PwY ---) PMHWY is a Pw-equivalence. Since PMHWY is W-null, we have Pw Y ~ PM HW Y as required. 5 with a nullity classification theorem for some nonsuspension spaces. 8. Let V, W E Ho* be finite 1-connected complexes such that typepV and typepW belong to {0,1,00} for all p. Then the condition (V) = (W) is equivalent to the joint conditions: (i) typepV = typepW for all p; (ii) connp V = connp W for all p. Proof. 7. The nullity classes covered by this theorem have canonical representatives of the form V M(Z/p, np) or sn V V M(Z/p, np) where J is a finite set of pEJ pEJ primes and n p , n 2 2 are integers with np < n for each p E J.

Lx is the image of a p-torsion class under the homomorphism n n TJ. 1. Proof. Let us write n n Hn(IT K(KjF,j); Z(p)) = Hn(Y x j=2 IT K(KjF,j); Z(p)) j=[~I+1 i. 12 K(KjF,j) and [il is the integral part of If j is odd, KjF ~ KjO, and if j is even:::; [i], Kj(F;Z(p)) ~ Kj(O;Z(p)) EB (81m K j _ 1 (O/rn; Z(p))) again by Corollary 1 of [B2], because [il :::; dp - 1. Therefore, for 2 :::; j :::; [i], Kj(F;Z(p)) is a direct sum of a free Z(prmodule of finite rank with an infinite direct sum of finite cyclic p-groups.

### Algebraic Topology: New Trends in Localization and Periodicity: Barcelona Conference on Algebraic Topology, Sant Feliu de Guíxols, Spain, June 1–7, 1994 by Martin Arkowitz, Gregory Lupton (auth.), Carles Broto, Carles Casacuberta, Guido Mislin (eds.)

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