Date: Mar 26, 2013 4:54 PM
Author: Axel Vogt
Subject: Re: Handling branch cuts in trig functions

Side remark: IIRC that view beyond branch cuts is named a holomorphic correspondence
(we are dim=1 here, so stems from a [branched] covering, all proper & discrete).
I can not remember that it was a beloved view (except in [old ?] Topology)

K. Stein, Maximale holomorphe und meromorphe Abbildungen.II Am. J. Math. 86, 823-868
K. Stein, Topics on holomorphic correspondences. Rocky Mt. J. Math. 2 (1972), 443-463