On manifolds with finitely generated homotopy groups
نویسندگان
چکیده
Let G be an infinite group which is finitely presented. Let X be a finite CW−complex of dimension q whose fundamental group is Z × G. We prove that for some i ≤ q the homotopy group πi(X) is not finitely generated. Let M be a manifold of dimension n whose fundamental group is Zn−2×G. Then the same conclusion holds (for some i ≤ maxn2 ] , 3 } ) unless M is an Eilenberg-McLane space. In particular, if G = Z×H and the homotopy groups of M are finitely generated, then M is homotopy equivalent to the n-torus. 2000 Mathematics Subject Classification: 57R70, 55P15, 57Q10
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تاریخ انتشار 2005