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Complex hyperbolic surfaces whose closed geodesics are all simple

Published 1 Oct 2026 in math.GT, math.AG, math.DG, and math.NT | (2610.01806v1)

Abstract: We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Prasad-Yeung, and Cartwright-Steger.

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