I am currently studying a basic course in algebraic topology.I am finding it difficult to understand the intuition behind the method of finding fundamental group of a simplicial complex using generators and relations.
"what is the context of finding a maximal tree L in a simplicial complex K and then considering K-L to find generators and relations?"
I think that after removing a maximal tree L(which is contractible) from a simplicial complex K,we are left with only loops,but cannot understand intuition behind construction of generators and relations to find out it's fundamental group.
for eg,consider triangulation K of torus
Here,The shaded region represents the subcomplex L.Then,how can we find fundamental group of torus considering K-L??what is the intuition behind the process of obtaining the fundamental group by considering K-L??
Any help would be appericiated...
