VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Homeomorphism and diffeomorphism groups of non-compact manifolds with the Whitney topology
    Banakh, Taras, 1968- ...
    For a non-compact ▫$n$▫-manifold ▫$M$▫ let ▫$\mathcal{H}(M)$▫ be the group of homeomorphisms of ▫$M$▫ endowed with the Whitney topology and ▫${\mathcal H}_c(M)$▫ the subgroup of ▫$\mathcal{H}(M)$▫ ... consisting of homeomorphisms with compact support. It is shown that the group ▫${\mathcal H}_c(M)$▫ is locally contractible and the identity component ▫${\mathcal H}_0(M)$▫ of ▫$\mathcal{H}(M)$▫ is an open normal subgroup in ▫${\mathcal H}_c(M)$▫. This induces the topological factorization ▫${\mathcal H}_c(M) \approx {\mathcal H}_0(M) \times {\mathcal M}_c(M)$▫ for the mapping class group ▫${\mathcal M}_c(M) = {\mathcal H}_c(M) / {\mathcal H}_0(M)$▫ with the discrete topology. Furthermore, for any non-compact surface ▫$M$▫, the pair ▫$({\mathcal H}(M), {\mathcal H}_c(M))$▫ is locally homeomorphic to ▫$(\square^\omega l_2,\boxdot^\omega l_2)$▫ at the identity ▫${\rm id}_M$▫ of ▫$M$▫. Thus the group ▫${\mathcal H}_c(M)$▫ is an ▫$(l_2 \times {\mathbb R}^\infty)$▫-manifold. We also study topological properties of the group ▫$\mathcal{D}(M)$▫ of diffeomorphisms of a non-compact smooth ▫$n$▫-manifold ▫$M$▫ endowed with the Whitney ▫$C^\infty$▫-topology and the subgroup ▫${\mathcal D}_c(M)$▫ of ▫$\mathcal{D}(M)$▫ consisting of all diffeomorphisms with compact support. It is shown that the pair ▫$({\mathcal D}(M), {\mathcal D}_c(M))$▫ is locally homeomorphic to ▫$(\square^\omega l_2,\boxdot^\omega l_2)$▫ at the identity ▫${\rm id}_M$▫ of ▫$M$▫. Hence the grou▫p ${\mathcal D}_c(M)▫$ is a topological ▫$(l_2 \times {\mathbb R}^\infty)$▫-manifold for any dimension ▫$n$▫.
    Vir: Topology proceedings. - ISSN 0146-4124 (Vol. 37, 2011, str. 61-93)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 15579225

    Povezava(-e):

    http://topology.auburn.edu/tp/restricted/v37/tp37004.pdf

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