A homological characterization of surface coverings
Tanabe, Masaharu
Proc. Japan Acad. Ser. A Math. Sci., Tome 84 (2008) no. 1, p. 170-173 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2008-09-15
Classification:  Homology groups,  Riemann surfaces,  surface coverings,  14H30,  30F30 
@article{1225463781,
     author = {Tanabe, Masaharu},
     title = {A homological characterization of surface coverings},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {84},
     number = {1},
     year = {2008},
     pages = { 170-173},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1225463781}
}

Tanabe, Masaharu. A homological characterization of surface coverings. Proc. Japan Acad. Ser. A Math. Sci., Tome 84 (2008) no. 1, pp.  170-173. http://gdmltest.u-ga.fr/item/1225463781/