CSE325 Assignment One: Surface Topology Q1 Suppose M is a closed triangle mesh. What is the definition of a cut graph of M ? How to find a cut graph ? Please give an algorithmic description. Q2 Suppose G is a graph, 1 (G) is the fundamental group of G. Does 1 (G) have any relator? If not, please explain the reason. How to compute 1 (G) ? Please give an algorithmic description. Q3 Suppose M is a closed mesh. Give an algorithmic description of computing the basis of the fundamental group of M . Q4 Give a mathematical proof for the algorithm you described in the answer to Q3. Hint: Use Seifert-van Kampen theorem to prove. 1