On the space of linear homeomorphisms of a polyhedral n-cell (Q1083725)

Let (D,T) be a closed n-cell with a triangulation T such that the triangulated cell is linearly embedded in the Euclidean space \(E^ n\). A linear homeomorphism of (D,T) is a homeomorphism \(f: D\to D\) such that f is pointwise fixed on Bd(D) and is linear on each simplex of T. The author shows that the space of all linear homeomorphisms of (D,T) has the structure of a fibre bundle with an open n-cell as its fibres. If the triangulation has exactly two interior vertices, the fibre bundle is homeomorphic to the product bundle \(E^ n\times E^ n\). This work is prompted by the problem raised by R. H. Bing and M. Starbird: under what conditions is a linear homeomorphism of \((D^ 2,T)\) linearly isotopic to the identity map of \(D^ 2\) ?