A homological characterization of surface coverings

Let f:X\to Y be a covering of closed oriented surfaces. Then f induces a homomorphism f_{*} :H_{1} (X,\mathbf{Z})\to H_{1} (Y,\mathbf{Z}) of the first homology groups. We consider the converse and characterize—in terms of matrices—the abstractly given homomorphisms of the first homology groups which...

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Veröffentlicht in:	Proceedings of the Japan Academy. Series A. Mathematical sciences 2008-11, Vol.84 (9), p.170-173
1. Verfasser:	Tanabe, Masaharu
Format:	Artikel
Sprache:	eng
Schlagworte:	14H30 30F30 Homology groups Riemann surfaces surface coverings
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creator	Tanabe, Masaharu
description	Let f:X\to Y be a covering of closed oriented surfaces. Then f induces a homomorphism f_{*} :H_{1} (X,\mathbf{Z})\to H_{1} (Y,\mathbf{Z}) of the first homology groups. We consider the converse and characterize—in terms of matrices—the abstractly given homomorphisms of the first homology groups which can be induced by coverings of prime degree. We also classify the induced homomorphisms in these cases.
doi_str_mv	10.3792/pjaa.84.170
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language	eng
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source	Project Euclid Open Access; Freely Accessible Japanese Titles; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete
subjects	14H30 30F30 Homology groups Riemann surfaces surface coverings
title	A homological characterization of surface coverings
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