DIKUL - logo
(UL)
  • A geometric criterion for the finite dimensionality of cell-like quotients of 4-manifolds
    Mitchell, William James Rae ; Repovš, Dušan, 1954- ; Ščepin, Evgenij V., 1951-
    We prove, for a proper, cell-like surjection ▫$f:M\to X$▫, defined on a topological 4-manifold ▫$M$▫, that ▫$\dim {X<\infty}$▫ (equivalently ▫$\dim {X = 4}$▫ if and only if for some ▫$n\geq 3$▫, ... ▫$X$▫ has the following general position property: for every ▫$\epsilon > 0$▫ and every collection of maps ▫$f_1,f_2,...,f_n:{D^2\to X}$▫ of the Pontrjagin disc ▫$D^2$▫ into ▫$X$▫, there exist maps ▫$g_1,g_2,...g_n:{D^2\to X}$▫ such that (i) for every ▫$i,d(f_i,g_i)<\epsilon$▫ and (ii) ▫${\bigcap}^n_{i=1} g_i(D^2) = \emptyset$▫. We also show that such an ▫$X$▫ is always four-dimensional if every compactum of cohomological dimension two is two-dimensional. As a corollary we prove that a cell-like quotient ▫$M/G$▫ of a topological 4-manifold ▫$M$▫ is finite-dimensional if ▫$M/G$▫ has Daverman's disjoint triples property.
    Vir: Preprint series of the Department of Mathematics. - ISSN 0352-3004 (Vol. 26, št. 248, 1988, str. 157-167)
    Vrsta gradiva - članek, sestavni del
    Leto - 1988
    Jezik - angleški
    COBISS.SI-ID - 7717634

Vnos na polico