K-theory and dynamics. II. (English) Zbl 0665.58038

Farrell, F. T.; Jones, L. E.

Ann. Math. (2) 126, 451-493 (1987).

This is the second part of the article [for the first part see ibid. 124, 531-569 (1986; Zbl 0653.58035)] where authors consider weakly admissible manifolds - i.e. manifolds with pinched negative curvature, and admissible manifolds - i.e. weakly admissible manifolds with finite volume. In this part of the article (as in the first one - using the dynamic of unit speed tangent bundle) they calculate the stable topological pseudo-isotopy space \({\mathcal P}(M)\) of an admissible manifold M: It is shown that if M is compact, then \({\mathcal P}(M)\) and \(\bar {\mathcal P}(S^ 1)\) are weakly homotopically equivalent, where \(\bar {\mathcal P}(S^ 1)\) is the direct limit as \(n\to \infty\) of the n-factor Cartesian product \({\mathcal P}(S^ 1)\times...\times {\mathcal P}(S^ 1)\). If M is not compact, \({\mathcal P}(\bar M)\) and \(\bar {\mathcal P}(S')\times {\mathcal P}(\partial \bar M)\) are weakly homotopically equivalent, where \(\bar M\) is a standard compactification of M.

Reviewer: V.Marenich

MSC:

37C10	Dynamics induced by flows and semiflows
18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
57R19	Algebraic topology on manifolds and differential topology
58J47	Propagation of singularities; initial value problems on manifolds
57R30	Foliations in differential topology; geometric theory

Keywords:

weakly admissible manifolds; pinched negative curvature; pseudo-isotopy space

Citations:

Zbl 0653.58035