I've been recently having a discussion on how to compute the genus of a pair of pants, namely the figure:
After some research, we stumbled across this webpage:
http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/model/euler.html
in which they find the genus of a three-holed sphere (i.e. a pair of pants) to be 2. However, the wikipedia article says it has genus 0.
https://en.wikipedia.org/wiki/Pair_of_pants_(mathematics)
For us, therefore, a satisfactory answer remains elusive. Our questions will then be: what are we missing? what is the right answer, if there is any (we hope so) ? What's the correct way to compute the genus of a pair of pants?
Thanks in advance!