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A Note on the Construction of a Set of Fundamental Circuits on a Surface of Genus p

Published online by Cambridge University Press:  20 November 2018

R. G. de Buda
R. G. de Buda*
Affiliation:
Canadian General Electric Co. Ltd.,Toronto, Ont.
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On an orientable surface of genus p, a set of 2p fundamental circuits can be selected which all pass through a single point A. After cutting along the 2p circuits, the surface can be unfolded into a flat region bounded by a 4p-gon so that: the set of vertices corresponds to the one point A; and the 2p pairs of edges to the 2p fundamental circuits; and the interior of the polygon to the remainder of the surface. If the edges of the polygon are directed, the 2 edges which correspond to one fundamental circuit will be directed in opposite sense, since the surface is orientable [1]. The sequence and direction of the edges is the same as the sequence of the fundamental circuits.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 1 , January 1961 , pp. 13 - 21
Copyright
Copyright © Canadian Mathematical Society 1961

References

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