Timeline for If H is a homeomorphism from $R^{n}$ to itself, and P and H(P) are compact polyhedra, is H(P) piecewise-linear homeomorphic to P?

5 events

when toggle format	what		by	license	comment
Mar 25, 2012 at 2:40	vote	accept	Ernest Davis
Mar 23, 2012 at 13:23	answer	added	Misha		timeline score: 4
Mar 23, 2012 at 4:42	comment	added	Misha		Suppose that $P, Q$ are $k$-dimensional polyhedra in ${\mathbb R}^n$ which are homeomorphic but not PL homeomorphic. If $2k+2\le n$ then the homeomorphism $f: P\to Q$ extends to a homeomorphism ${\mathbb R}^n\to {\mathbb R}^n$ by H.Gluck's theorem 1.3 from his "Embeddings in the trivial range" paper (Annals of Math., 1965). Gluck's result deals with embeddings to general manifolds, so the case when the target is ${\mathbb R}^n$ may have been known earlier.
Mar 23, 2012 at 3:35	history	edited	Ernest Davis	CC BY-SA 3.0	question misstated in title
Mar 23, 2012 at 1:32	history	asked	Ernest Davis	CC BY-SA 3.0