4
votes
0answers
75 views

Bases of surface groups

Let $\Gamma_g$ be a surface group of genus $g \geq 2$. A $2g$-tuple $(x_1,y_1, \dots,x_g,y_g) \in \Gamma_g^{2g}$ will be called a Surface Basis if we have the presentation $$\Gamma_g = \langle x_1, ...
1
vote
1answer
174 views

Lefschetz numbers for homomorphisms of free groups

Let $G = F_X$ be the free group on a finite set $X$, and $\phi\colon G\to G$ a group homomorphism. Consider the number $$ \sum_{x\in X} (\text{number of occurrences of the generator $x$ in the word ...