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We prove that for each sufficiently complicated orientable surface $S$, thereexists an infinite image linear representation $\rho$ of $\pi_1(S)$ such thatif $\gamma\in\pi_1(S)$ is freely homotopic to a simple closed curve on $S$,then $\rho(\gamma)$ has finite order. Furthermore, we prove that given asufficiently complicated orientable surface $S$, there exists a regular finitecover $S'\to S$ such that $H_1(S',\mathbb{Z})$ is not generated by lifts ofsimple closed curves on $S$, and we give a lower bound estimate on the index ofthe subgroup generated by lifts of simple closed curves. We thus answer twoquestions posed by Looijenga, and independently by Kent, Kisin, March\'e, andMcMullen. The construction of these representations and covers relies onquantum $\text{SO}(3)$ representations of mapping class groups.

Quotients of surface groups and homology of finite covers via quantum representations