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Immersions of Pants into a Fixed Hyperbolic Surface | Lewis Bowen
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23 May 2005 | Subject: | Geometric Topology; Dynamical Systems MSC-class: 20E09, 20F69, 37E35, 51M10 | math.GT math.DS | Abstract: | Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T_1(S) x T_1(S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two uniformly random closed geodesics gamma_1, gamma_2 of length within epsilon of L have a high probability of partially bounding an immersed 4-holed sphere whose other boundary components also have length within epsilon of L. Version 2: The coefficient in corollary 1.6 corrected from 16 to 8. | Source: | arXiv, math.GT/0505480 | Services: | Forum | Review | PDF | Favorites |
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