I have read a lot of books and a lot of posts in the Internet and I still can't understand few problems. Professor, who presents us a lecture "Algebraic topology", is doing his job like he must to do it. Moreover, he just translates Munkres book "Algebraic topology" without any explanation.
Back to the issue. I have an exam in next week and example exercises.
- Find a complex with 7 vertices whose underlying space is Torus.
- Find a complex with 8 vertices whose underlying space is Klein Bottle.
I know Torus and Klein Bottle fundamental polygons and I saw an example triangulations of both of this surfaces. How to solve these exercises with only the fundamental polygons (https://commons.wikimedia.org/wiki/Fundamental_polygon)? How to build this complexes?
Thanks for any hint.