Finiteness properties of classifying spaces of proper Λ-actions

Connolly, Frank; Koźniewski, Tadeusz

doi:10.1016/0022-4049(86)90097-6

“…PROOF. Since VcdT < oo and by hypothesis MH is contractible for each finite subgroup H of T, so by [8], M is of type £T. By Corollary 3.9, M is r-homeomorphic to U(T,Q), where Q is a compact admissible manifold.…”

Section: Proposition 12 [1 P 19] Let G E Tmentioning

confidence: 88%

Rigidity Theorems for Right Angled Reflection Groups

Rosas¹

1988

Transactions of the American Mathematical Society

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“…Thus for any j ~ 0 the space .9'j(g') may be taken to be the space of stable pseudoisotopies of g' x R j which have compact support in the g' -factor and which are bounded in the R j -factor; that is, we do not need to refer to the semisimplicial construction for . 9…”

Section: Prooj Oj Lemma 32 In Order To Conserve On Notation We Willmentioning

confidence: 99%

“…If X is a manifold and i ~ 0 an integer, then we denote by pb (X x Ri) the space of all topological pseudoisotopies h: X x Ri X [0, 1] --+ X X Ri X [0, 1], which are bounded in the Ri -factor and have compact support in the X -factor. (Recall that h is a topological pseudoisotopy if it is a homeomorphism such that hlX x Ri x 0 = inclusion and that h is bounded in the Ri -factor if there is a number a > 0 such that for all (x, y, t) E X X Ri X [0, 1] we have that Iy -/1 ~ a holds where .9,(X) to be the direct limit space limitq~ocpb(X X I q X R i ), and for integers i < 0 set 9…”

Section: The Isomorphism Conjecturesmentioning

confidence: 99%

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Isomorphism conjectures in algebraic 𝐾-theory

Farrell¹,

Jones²

1993

J. Amer. Math. Soc.

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In this paper we are concerned with the four functors .9*, .9: iff , ~ , and £:-00 , which map from the category of topological spaces X to the category d'ff of n-spectra. The functor .9* ( ) (or .9* 1 ( )) maps the space X to the nspectrum of stable topological (or smooth) pseudoisotopies of X. (The spaces .9 i (X) , .9 i diff (X) , i ;::: 0, are Hatcher's deloopings of .9 0 (X) , .9~iff(X) (cf.[29])). The functor ~() maps a path-connected space X to the algebraic Ktheoretic n-spectrum for the integral group ring Z1l, X. (The spaces ~ (X) , i ;::: 0, are the Gersten-Wagoner deloopings of ~(X); cf. [27,52].) ~(X) is also defined on a nonpath-connected space X to be EBiEI~(Xi)' where {Xi: i E /} are the path components of X and EB iEI ~ (Xi) indicates the direct limit of all finite products of the {~(Xi): i E I}. If X is path connected then the functor £:-00 () maps X to the L -00 -surgery classifying spaces for oriented surgery problems with fundamental group 1l, X identified by their fourfold periodicity ~-OO(X) = ~~~(X) (cf. [35,39,44,47]). In addition, if X is not path connected then we set £:-OO(X) = EBiE1£:-00(X i ) , where {Xi: i E i} are the path components of X.

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“…(Note that we do not require h to have compact support in the factor g.) For j < 0 we set .9'j(g) = n-j . 9…”

Section: " (T)mentioning

confidence: 99%

Untitled

1993

J. Amer. Math. Soc.

0

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In this paper we are concerned with the four functors .9*, .9: iff , ~ , and £:-00 , which map from the category of topological spaces X to the category d'ff of n-spectra. The functor .9* ( ) (or .9* 1 ( )) maps the space X to the nspectrum of stable topological (or smooth) pseudoisotopies of X. (The spaces .9 i (X) , .9 i diff (X) , i ;::: 0, are Hatcher's deloopings of .9 0 (X) , .9~iff(X) (cf.[29])). The functor ~() maps a path-connected space X to the algebraic Ktheoretic n-spectrum for the integral group ring Z1l, X. (The spaces ~ (X) , i ;::: 0, are the Gersten-Wagoner deloopings of ~(X); cf. [27,52].) ~(X) is also defined on a nonpath-connected space X to be EBiEI~(Xi)' where {Xi: i E /} are the path components of X and EB iEI ~ (Xi) indicates the direct limit of all finite products of the {~(Xi): i E I}. If X is path connected then the functor £:-00 () maps X to the L -00 -surgery classifying spaces for oriented surgery problems with fundamental group 1l, X identified by their fourfold periodicity ~-OO(X) = ~~~(X) (cf. [35,39,44,47]). In addition, if X is not path connected then we set £:-OO(X) = EBiE1£:-00(X i ) , where {Xi: i E i} are the path components of X.

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Finiteness properties of classifying spaces of proper Λ-actions

Cited by 24 publications

References 12 publications

Rigidity Theorems for Right Angled Reflection Groups

Rigidity Theorems for Right Angled Reflection Groups

Isomorphism conjectures in algebraic 𝐾-theory

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