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Original Articles

Self-Intersection Numbers of Curves in the Doubly Punctured Plane

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Pages 26-37 | Received 21 Jul 2010, Accepted 27 Jun 2011, Published online: 13 Mar 2012

REFERENCES

  • Basmajian , [Basmajian 93] A. 1993 . “The Stable Neighborhood Theorem and Lengths of Closed Geodesics” . Proc. Amer. Math. Soc. , 119 ( 1 ) : 217 – 224 .
  • Chas , [Chas and Lalley 12] M. and Lalley , S. 2012 . “Self-Intersections in Combinatorial Topology: Statistical Structure” . arXiv , : 1012.0580v1[math.GT] to appear in Invent. math.
  • Chas , [Chas and Phillips 10] M. and Phillips , A. 2010 . “Self-Intersection of Curves on the Punctured Torus” . Exp. Math , 19 : 129 – 148 .
  • Cohen , [Cohen and Lustig 87] M. and Lustig , M. 1987 . “Paths of Geodesics and Geometric Intersection Numbers I” . In Combinatorial Group Theory and Topology, Alta, Utah, 1984, Ann. of Math. Studies 111 , 479 – 500 . Princeton Univ. Press .
  • Hass , [Hass and Scott 85] J. and Scott , P. 1985 . “Intersections of Curves on Surfaces” . Israel J. Math. , 51 : 90 – 120 .
  • Lalley , [Lalley 96] S. 1996 . “Self-Intersections of Closed Geodesics on a Negatively Curved Surface: Statistical Regularities” . In Convergence in Ergodic Theory and Probability (Columbus, OH, 1993), Ohio State Univ. Math. Res. Inst. Publ., 5 , 263 – 272 . De Gruyter .
  • Mirzakhani , [Mirzakhani 08] M. 2008 . “Growth of the Number of Simple Closed Geodesics on a Hyperbolic Surface” . Ann. of Math. , 168 : 97 – 125 .

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