I will start learning about character varieties. I need to learn about Teichmuller spaces and how to consider them as components of "some character variety".
Can someone recommend some textbooks or papers, please? Thanks.
I will start learning about character varieties. I need to learn about Teichmuller spaces and how to consider them as components of "some character variety".
Can someone recommend some textbooks or papers, please? Thanks.
William Goldman has proven that the components of the character variety of the fundamental group of a surface $S$ into $PSL_2(\mathbb{R})$ are in one-to-one correspondence with the induced Euler classes of the representations (which by the Milnor-Wood inequality are $\leq |\chi(S)|$), with the maximal and minimal Euler classes corresponding to copies of Teichmuller space. Have a look at his paper and references therein.