Monodromy Theorem

If a complex function  is analytic in a disk contained in a simply connected domain  and  can be analytically continued along every polygonal arc in , then  can be analytically continued to a single-valued analytic function on all of !

REFERENCES:

Flanigan, F. J. Complex Variables: Harmonic and Analytic Functions. New York: Dover, p. 234, 1983.

Knopp, K. "The Monodromy Theorem." §25 in Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, pp. 105-111, 1996.

Krantz, S. G. "The Monodromy Theorem." §10.3.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 134, 1999.