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

Central to this choice of papers are new advancements within the basic conception of localization of areas. This box has gone through great switch of past due and is yielding new perception into the mysteries of classical homotopy conception. the current quantity includes the refereed articles submitted on the convention on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. a number of accomplished articles on common localization make clear the elemental instruments and provides a file at the cutting-edge within the material. The textual content is as a result obtainable not just to the pro mathematician but in addition to the complex student.

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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

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Remember that Hn(SL(O); Z) is a finitely generated abelian group for all n ;::: 0, while Hn(SL(F);Z) is not finitely generated. However, it was shown in Section 2 of [AI] that Hn(SL(F); Z) is the direct sum of a free abelian group of finite (and known) rank and a torsion group. Some information about this torsion *) The second author wishes to thank the Swiss National Science Foundation for financial support while this research was being carried out. 24 Dominique Arlettaz and Piotr Zelewski group is given in [AZ], where we prove that for any n 2:: 0, it contains finitely many non-trivial divisible homology classes.

4 to show that nm(fibg) is E*-acyclic for all m. When E = K(l) or KZlp, we have convenient homotopical criteria for durability. S. A map g : X --+ Y in H0 3 is a durable K(l)*-equivalance (or K* (-; Z Ip)-equivalence) if and only if it satisfies the following equivalent conditions: (i) g* : V 117r*(X; Zip) ~ V 117r*(Y; Zip); (ii) conn VI + 2.

K. 4. For a space X E Ho* and n p-torsion space with -1 Vm Jr* (P~ X. v, n )~ , m-1 - 2': 1, PnX is an n-connected {V'-lJr 1) n * (X,V, n0 Since the cofibre of w : ~dVn_1 --t 'or m = n formf=n. J' Vn - 1 has p-type n + 1, we find for n 2': 1 and t 2': 2, so that the vn-periodic~homotopy groups of X are exposed as ordinary homotopy groups of PnX and PnX. 5. A STABLE CHROMATIC TOWER. 12) of E for a p-torsion finite CW-spectrum Wn of ptype n + 1. This tower must be distinguished from Ravenel's original chromatic tower {LnE}n>o in view of his refutation of the telescope conjecture.

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