Year: 1985
Type: article
Abstract: Let $M$ and $F$ be Hilbert cube manifolds with $F$ compact. The purpose of this paper is to study homotopy equivalences $f:M \to {{\mathbf {R}}^m} \times F$ which have bounded control in the ${{\mathbf {R}}^m}$-direction. Roughly, these homotopy equivalences form a semi-simplicial complex $\mathcal {W}\mathcal {H}({{\mathbf {R}}^m} \times F)$, the controlled Whitehead space. Using results about approximate fibrations, $\mathcal {W}\mathcal {H}({{\mathbf {R}}^m} \times F)$ is related to the semi-simplicial complex of bounded concordances on ${{\mathbf {R}}^m} \times F$. Then the homotopy groups of $\mathcal {W}\mathcal {H}({{\mathbf {R}}^m} \times F)$ are computed in terms of the lower algebraic $K$-theoretic functors ${K_{ - i}}$.
Author: C. Bruce Hughes
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1993673539