The Ninth Week: Covering surfaces and fundamental groups

Michio Kuga

A chapter in Galois’ Dream: Group Theory and Differential Equations, 1993, pp 59-60 from Springer

Abstract: Abstract Let f: D’ → D be a covering. Since f is a continuous map, when a point P in D’ moves continuously over a figure F of D’, f (P) = Q moves continuously in D. Let f (F) be the figure in D which Q traces out. In particular, if P traces a curve C in D’, then the trace f (C) of the point f (P) = Q is again a curve in D. If C is a closed curve, then f (C) is also a closed curve.

Date: 1993
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DOI: 10.1007/978-1-4612-0329-2_10

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