English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For a non-compact n-manifold M let H(M) denote the group of homeomorphisms ofM endowed with the Whitney topology and H_c(M) the subgroup of H(M) consistingof homeomorphisms with compact support. It is shown that the group H_c(M) islocally contractible and the identity component H_0(M) of H(M) is an opennormal subgroup in H_c(M). This induces the topological factorization H_c(M)\approx H_0(M) \times \M_c(M) for the mapping class group \M_c(M) =H_c(M)/H_0(M) with the discrete topology. Furthermore, for any non-compactsurface M, the pair (H(M), H_c(M)) is locally homeomorphic to (\square^wl_2,\cbox^w l_2) at the identity id_M of M. Thus the group H_c(M) is an (l_2\times R^\infty)-manifold. We also study topological properties of the groupD(M) of diffeomorphisms of a non-compact smooth n-manifold M endowed with theWhitney C^\infty-topology and the subgroup D_c(M) of D(M) consisting of alldiffeomorphisms with compact support. It is shown that the pair (D(M),D_c(M))is locally homeomorphic to (\square^w l_2, \cbox^w l_2) at the identity id_M ofM.  Hence the group D_c(M) is a topological (l_2 \times R^\infty)-manifold forany dimension n.

Homeomorphism and diffeomorphism groups of non-compact manifolds with the Whitney topology