Open Access
November 2008 A homological characterization of surface coverings
Masaharu Tanabe
Proc. Japan Acad. Ser. A Math. Sci. 84(9): 170-173 (November 2008). DOI: 10.3792/pjaa.84.170


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.


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Masaharu Tanabe. "A homological characterization of surface coverings." Proc. Japan Acad. Ser. A Math. Sci. 84 (9) 170 - 173, November 2008.


Published: November 2008
First available in Project Euclid: 31 October 2008

zbMATH: 1160.14017
MathSciNet: MR2483602
Digital Object Identifier: 10.3792/pjaa.84.170

Primary: 14H30
Secondary: 30F30

Keywords: homology groups , Riemann surfaces , surface coverings

Rights: Copyright © 2008 The Japan Academy

Vol.84 • No. 9 • November 2008
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