{'fraction_non_alphanumeric': 0.0205761316872428, 'fraction_numerical': 0.00411522633744856, 'mean_word_length': 5.083333333333333, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Prising apart geodesics by length in hyperbolic manifolds

Abstract We develop a condition on a closed curve on a surface or in a 3-manifold that implies that the length function associated to the curve on the space of all hyperbolic structures on the surface or in the 3-manifold (respectively) completely determines the curve. Specifically, for an orientable surface S of negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case arising from hyperellipticity that we describe completely). For a large class of hyperbolizable 3-manifolds, we show that curves freely homotopic to simple curves on ∂M have this property.