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

Central to this selection of papers are new advancements within the common concept of localization of areas. This box has gone through great swap of overdue and is yielding new perception into the mysteries of classical homotopy thought. 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 finished articles on common localization make clear the fundamental instruments and provides a record at the cutting-edge within the subject material. The textual content is for this reason available not just to the pro mathematician but additionally to the complicated student.

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Extra info 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

6. There are induced isomorphisms JriPnOOO E ~ JriOOO L~E and Jr}JnOOO E ~ JriOOO M~E for i > connp V n + 2. Proof. For Wn = ~oo(~V n), the [Wn' -]*-trivialization of E is given by the homotopy colimit of the ~-kWn-nullifications of E as k --t 00. 10, for i > connp V n + 2. 6 The monochromatic homotopy categories Working over a fixed prime p for n 2': 1, we let PnHo* C Ho* and M~Hos C H OS be the full subcategories whose objects are equivalent to the nth chromatic layers PnX and M~ E of spaces X E H 0* and spectra E E H os.

By Mitchell [26] or Hopkins-Smith [21], for each positive integer TI, there exists a finite p-torsion complex of p-type n. We say that two spaces X, Y E H 0* have the same stabilized nullity if (X) :2 (~iy) and (Y) :2 (~j X) for some l, j :2 0. The resulting stabilized nullity classes {X} are partially ordered with finite wedge and smash operations. 4. finite connected complexes V, vV E Ho*. the condition {V} = {W} holds if and only ~f typepV = typc p W fOT each pTime p. Proof. Taking suspensions, we can assume that V and Ware 1-conrwcted.

For spectra W, X E Hos, if PwX GEM with a canonical H -module structure. THEOREM ~ 0, then PI;WX is a stable This immediately generalizes to f-Iocalizations. For p prime and nEZ, we say that a spectrum W satisfies the n-supported p-torsion condition when H* W is (n-l)-connected p-torsion with Hn(W; Zip) i o. 6. For spectra W, X E Ho S and i E Z, the fibre F of the Postnikov map PI;i+1WX -+ PI;iWX is a stable GEM with a canonical H-module structure. Moreover, when W satisfies the n-supported p-torsion condition, then F ~ En+iHG for some p-torsion abelian group G.

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