Fibrations with Hopfian properties |
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Authors: | A J Berrick |
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Institution: | (1) Department of Mathematics, National University of Singapore, 0511 Kent Ridge, Singapore |
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Abstract: | This study explores the homotopy-theoretic meeting-point of topics in differential topology, combinatorial group theory and
algebraicK-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. LetF (
→
ί
)E →B be a fibration such thati induces an isomorphism of homology with trivial integer coefficients; what is the effect ofi on fundamental groups? In particular, when one passes to hypoabelianisations by factoring out perfect radicals, doesi 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. |
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Keywords: | |
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