Celebratio Mathematica — Kirby — Complete Bibliography

Complete Bibliography

Works connected to Robert Duncan Edwards

Filter the Bibliography List

year	title	people

			clear

R. D. Edwards and R. C. Kirby: “Deformations of spaces of imbeddings,” Ann. Math. (2) 93 : 1 (January 1971), pp. 63–88. MR 283802 Zbl 0214.50303 article

In [1969], the second author proved that homeomorphisms of the torus \( T^n \) (the \( n \)-fold product of circles) are stable and used this fact, along with an immersion of \( T^n \) minus a point into \( \mathbb{R}^n \), to prove that the homeomorphism group of \( \mathbb{R}^n \) (with the compact-open topology) is locally contractible. This paper generalizes the techniques of that paper and applies them to arbitrary manifolds. The main theorem of the paper says that if \( U \) is a subset of a manifold \( M \) containing a compact subset \( C \) in its interior, then given any two sufficiently close proper imbeddings \[ h_0,g_0:U\to M \] of \( U \) into \( M \), there is a canonical proper isotopy \[ h_t:U\to M , \quad t\in I ,\] connecting \( h_0 \) to an imbedding \( h_1 \), which agrees with \( g_0 \) on \( C \). Furthermore, the isotopy is fixed on the complement of a compact neighborhood of \( C \) in \( U \).