Examples 3.13
(a)
Let M = S
1
with the charts:
x = arg(z),
= arg(
-
z)
discussed in Lecture 2. There, we saw that the change-of-coordinate maps, are given by
x
=
+
if
<
-
if
>
=
+
x
if
x <
-
x
if
x >
,