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We prove that for every nonnegative integer $g$, there exists a bound on thenumber of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ ofgenus $g$ and finite topology. This bound on the finite number of ends when $M$has at least two ends implies that $M$ has finite stability index which isbounded by a constant that only depends on its genus.

Bounds on the topology and index of minimal surfaces