Euler Characteristics and the Classification of Closed Surfaces Flashcards
1
Q
Define Euler Characteristic of a finite graph
A
2
Q
What is X(G) for a finite tree
A
3
Q
What is X(G) for a finite connected graph
A
4
Q
State Euler’s Theorem
A
5
Q
State Corollary of Euler’s Theorem
A
6
Q
Define a good graph and it’s G Euler characterstic
A
7
Q
State the Euler Charactersitic of a surface
A
8
Q
State the Union Lemma
A
9
Q
What is the Euler Charaterstic of a connected sum
A
10
Q
State the effect of adding the handles and cross caps on the euler charactersitic
A
11
Q
Define thickening
A
12
Q
Give basic facts about the thickening
A
13
Q
What is the euler characteristic of a thickening
A
14
Q
Define the dual graph
A
15
Q
Give the first 3 props of the dual graph
A
16
Q
State the classification theorem
A
17
Q
What do we know about the euler characteristic of a simplicial complex that triangulates a closed surface
A
