منابع مشابه
Notes on Serre fibrations
Here the solid arrows represent maps that are given, and the problem is to find a map h commuting in the diagram. Usually the map i is an inclusion, and p is some kind of “bundle map” such as a local product. Note the special cases: (i) if i is an inclusion, E = A, and f = 1A, then the extension problem asks whether A is a retract of X; and (ii) if p is surjective, X=B, and g = 1B, the lifting ...
متن کاملHexagons for Noncommutative Serre Fibrations *
We introduce in this paper the notions of noncommutative (shortly, NC) CW-complex, noncommutative Serre fibration and show that up to homo-topy, every NC CW-complex algebra morphism is some noncommutative Serre fibration. We then deduce a six-term exact sequence for the periodic cyclic homology and for K-theory of an arbitrary noncommutative Serre fi-bration, or of a morphism in the category of...
متن کاملSpectral Sequences for Noncommutative Serre Fibrations
We prove in this paper a noncommutative version of Leray Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with E2 terms as E2 p,q = HPp(A;HPq(B,A)) =⇒ HPp+q(B) and E 2 p,q = HPp(A;Kq(B,A)) =⇒ Kp+q(B). Introduction The ideas of using spectral sequences to operator algebras was started in [C]. In that...
متن کاملSpectral Sequences for Noncommutive Serre Fibrations
We prove in this paper a noncommutative version of Leray Theorem and then Serre Spectral Theorem for noncommutative Serre fibrations. We prove that for NC Serre fibration there are converging spectral sequences with E2 terms as E2 p,q = HPp(B,A;HPq(A)) =⇒ HPp+q(B) and E 2 p,q = HPp(B,A;Kq(A)) =⇒ Kp+q(B). Introduction The ideas of using spectral sequences to operator algebras was started in [C]....
متن کاملFibrations and Homotopy Colimits of Simplicial Sheaves
We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the no...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1981
ISSN: 0373-0956
DOI: 10.5802/aif.838