We study the homotopy type of closed connected orientable topological 4-manifolds M with Lambda-free second homotopy group, where Lambda is the integral group ring of pi_1(M). This is related with problem N.4.53 of [R. Kirby, Contemporary Math., 35 (1984)], and extends some results proved for the class of closed 4-manifolds with free fundamental group. Other applications on special classes of closed topological manifolds complete the paper.
Four-manifolds with π1-free second homotopy / Spaggiari, Fulvia. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 111:(2003), pp. 303-320. [10.1007/s00229-003-0371-7]
Four-manifolds with π1-free second homotopy
SPAGGIARI, Fulvia
2003
Abstract
We study the homotopy type of closed connected orientable topological 4-manifolds M with Lambda-free second homotopy group, where Lambda is the integral group ring of pi_1(M). This is related with problem N.4.53 of [R. Kirby, Contemporary Math., 35 (1984)], and extends some results proved for the class of closed 4-manifolds with free fundamental group. Other applications on special classes of closed topological manifolds complete the paper.
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