Genus sets and SNT sets of certain connective covering spaces

Volume 195 / 2007

Huale Huang, Joseph Roitberg Fundamenta Mathematicae 195 (2007), 135-153 MSC: 55P60, 55P62, 55P15, 20G99. DOI: 10.4064/fm195-2-3


We study the genus and SNT sets of connective covering spaces of familiar finite CW-complexes, both of rationally elliptic type (e.g. quaternionic projective spaces) and of rationally hyperbolic type (e.g. one-point union of a pair of spheres). In connection with the latter situation, we are led to an independently interesting question in group theory: if $f$ is a homomorphism from ${\rm Gl}(\nu, A)$ to ${\rm Gl}(n,A)$, $\nu < n$, $A=\mathbb{Z}$, resp. $\mathbb{Z}_p$, does the image of $f$ have infinite, resp. uncountably infinite, index in ${\rm Gl}(n,A)$?


  • Huale HuangIBM Global Services
    Morristown, NJ, U.S.A.
    283 King George Rd.
    Warren, NJ 07059, U.S.A.
  • Joseph RoitbergDepartment of Mathematics & Statistics
    Hunter College, CUNY
    695 Park Ave., New York, NY 10021, U.S.A.
    Ph.D. Program in Mathematics
    The Graduate Center, CUNY
    365 Fifth Ave., New York, NY 10036, U.S.A.

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