Diffeomorphism groups of non-compact manifolds endowed with the Whitney C∞-topology

Suppose M is a non-compact connected n-manifold without boundary, D(M) is the group of C-infinity-diffeomorphisms of M endowed with the Whitney C-topology and D-0(M) is the identity connected component of D(M), which is an open subgroup in the group D-c(M) subset of D(M) of compactly supported diffeomorphisms of M. It is shown that D0(M) is homeomorphic to N x R-infinity for an l(2)-manifold N whose topological type is uniquely determined by the homotopy type of D-0(M). For instance, Do(M) is homeornorphic to l(2) x R-infinity if n = 1,2 or n = 3 and M is orientable and irreducible. We also show that for any compact connected n-manifold N with non-empty boundary UN the group D-0(N\partial derivative N) is homeomorphic to D-0(N;partial derivative N) x R-infinity, where D-0(N;partial derivative N) is the identity component of the group D(N;partial derivative N) of diffeomorphisms of N that do not move points of the boundary partial derivative N. (C) 2014 Elsevier B.V. All rights reserved.