Geodesic
Genus sets and SNT sets of certain connective covering spaces
Huale Huang 1   ; Joseph Roitberg 2
1 IBM Global Services Morristown, NJ, U.S.A. and Citigroup 283 King George Rd. Warren, NJ 07059, U.S.A.
2 Department of Mathematics & Statistics Hunter College, CUNY 695 Park Ave., New York, NY 10021, U.S.A. and Ph.D. Program in Mathematics The Graduate Center, CUNY 365 Fifth Ave., New York, NY 10036, U.S.A.
Fundamenta Mathematicae, Tome 195 (2007) no. 2, pp. 135-153 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\rm Gl}(n,A)$?
DOI : 10.4064/fm195-2-3
Keywords: study genus snt sets connective covering spaces familiar finite cw complexes rationally elliptic type quaternionic projective spaces rationally hyperbolic type one point union pair spheres connection latter situation led independently interesting question group theory homomorphism mathbb resp mathbb does image have infinite resp uncountably infinite index

Huale Huang  1   ; Joseph Roitberg  2

1 IBM Global Services Morristown, NJ, U.S.A. and Citigroup 283 King George Rd. Warren, NJ 07059, U.S.A.
2 Department of Mathematics & Statistics Hunter College, CUNY 695 Park Ave., New York, NY 10021, U.S.A. and Ph.D. Program in Mathematics The Graduate Center, CUNY 365 Fifth Ave., New York, NY 10036, U.S.A. 
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Huale Huang; Joseph Roitberg. Genus sets and SNT sets of certain connective covering spaces. Fundamenta Mathematicae, Tome 195 (2007) no. 2, pp. 135-153. doi: 10.4064/fm195-2-3

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