“…Given excision, homotopy invariance is equivalent to showing that C * r B G (CX + × [0, 1); C) has trivial K-theory. The proof of this follows the arguments of [ACFP94], see also [HPR97].…”
Section: Theorem 74 ([Ped00 41]) the Continuously Controlled Assementioning
confidence: 61%
“…From our point of view, the primary assembly map (see § 7) is constructed from functors on the continuously controlled categories introduced in [ACFP94]. In § 2 we give some basic material on spectra and introduce the main examples of geometric interest.…”
Abstract. In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K-and L-theory, and C * -theory.
“…Given excision, homotopy invariance is equivalent to showing that C * r B G (CX + × [0, 1); C) has trivial K-theory. The proof of this follows the arguments of [ACFP94], see also [HPR97].…”
Section: Theorem 74 ([Ped00 41]) the Continuously Controlled Assementioning
confidence: 61%
“…From our point of view, the primary assembly map (see § 7) is constructed from functors on the continuously controlled categories introduced in [ACFP94]. In § 2 we give some basic material on spectra and introduce the main examples of geometric interest.…”
Abstract. In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K-and L-theory, and C * -theory.
“…In particular, using coarse structures arising from 'continuous control at infinity' (see [1]) we obtain a result on the Novikov conjecture that appears to be new.…”
In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of "coarse CW -complexes". This uniqueness result is used to prove a version of the coarse Baum-Connes conjecture for such spaces.
“…We shall denote this category by cX Y bY R. The subcategory of isomorphisms is also symmetric monoidal and has an associated spectrum cX Y bY R will be denoted by KX Y bY R. Note that if b is the bornology associated to a metric, then cX Y bY R coincides with the bounded category cX Y R of [15] applied to the metric space X . If bX Y dX is the continuously controlled bornology associated to a compacti¢cation X of X then cX Y bX Y dX Y R is the continuously controlled category bX Y dX Y R of [2] and [5]. For brevity we shall continue to use the notation bX Y dX Y R for cX Y bX Y dX Y R.…”
Section: Bounded K-theory and K-theory With Continuous Control At Imentioning
confidence: 99%
“…We shall use m to denote the category whose objects are quadruples X Y dX Y Y S, where X Y dX is a compact Hausdorff pair, where P RCdX , and where S is a finite subset of dX . A morphism from 2 in m so that 1 refines RCf jdX 1 2 , and so that f S 1 S 2 . Any functor F X m 3 spectra determines a functor F X cE 3 spectra on objects via the formula…”
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