3 problems

Index-bound conjecture. One has

Let $Y$ be an oriented rational homology 3-sphere with an involution or finite-order diffeomorphism $\tau$ as in the paper’s main theorem, and let $\operatorname{Lef}(\tau_*)$ deno…

Let $Y$ be a rational homology sphere with a diffeomorphism $\tau:Y\to Y$ of order $n\geq 2$. Suppose that the quotient $Y/\tau$ is an integral homology sphere $Y'$ and that the br…