Riemann surfaces
1.1. Riemann surfaces
Let us start from the concept of a topological manifold.
Definition. An n-dimensional topological manifold M is a Hausdo
with a countable basis for its topology with the property that ev
a G M has an open neighborhood U which is homeomorphic to
neighborhood V of
W1.
A homeomorphism ip : U V\ U C M open, F c R
n
open,
chart
A family 21 = {(pi : Ui V{}iei of charts is called an atl
U

/ Ui = M.
Let pi : Ui - Vi, (p2 : U2 -+ V2 be two charts with U\ fl U2
Figure 1.1. Transition function
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