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|Title:||Fibrations with Hopfian properties||Authors:||Berrick, A.J.||Issue Date:||Dec-1989||Citation:||Berrick, A.J. (1989-12). Fibrations with Hopfian properties. Israel Journal of Mathematics 66 (1-3) : 41-53. ScholarBank@NUS Repository. https://doi.org/10.1007/BF02765885||Abstract:||This study explores the homotopy-theoretic meeting-point of topics in differential topology, combinatorial group theory and algebraic K-theory. The first two are due to H. Hopf and date from around 1930. The third arose in the author's characterisation of plus-constructive fibrations. Let F ( → ί )E →B be a fibration such that i induces an isomorphism of homology with trivial integer coefficients; what is the effect of i on fundamental groups? In particular, when one passes to hypoabelianisations by factoring out perfect radicals, does i induce an epimorphism? Numerous conditions are determined which force an affirmative answer. On the other hand, negative examples of a non-finitary nature are also provided. This leaves the question open in the finitely generated case, where it forms a homological version of the dual to Hopf's original, famous question in group theory. © 1989 The Weizmann Science Press of Israel.||Source Title:||Israel Journal of Mathematics||URI:||http://scholarbank.nus.edu.sg/handle/10635/103268||ISSN:||00212172||DOI:||10.1007/BF02765885|
|Appears in Collections:||Staff Publications|
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