What is meant by "side of a curve"? I'm currently reading "A primer on mapping class groups" by Farb-Magalit. A notion that often turns up is that of a "side of a curve". For example in the proof of Proposition 3.2 or in the proof that the center of the mapping class group of $S_g$ is trivial, whenever $g \geq 3$.
I just can't seem to find any definition for "side" of a curve online. Also, what is meant by "two edges"? I can imagine what edges should be, when we build a simplex of 2 points and 2 edges, but with one point and one edge?
$Z(MCG(S_g)) \cong 1$" />

It is related with the regular neighborhood of the curve: a simple closed curve in an orientable surface has as a regular neighborhood an annular subsurface, while in a non orientable surface a regular neighborhood it will be a Möbius band.
The boundary of a regular neighbourhood of an annular subsurface has two components while a Möbius strip has one.
