The good pants homology and the Ehrenpreis Conjecture

Abstract

We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces. (Good pants are pairs of pants whose cuffs have the length nearly equal to some large number $R>0$.) Combined with our previous work on the Surface Subgroup Theorem, this yields a proof of the Ehrenpreis Conjecture.

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  • [bowen] L. Bowen, Weak forms of the Ehrenpreis conjecture and the surface subgroup conjecture.
    @misc{bowen,
      author = {Bowen, L.},
      title = {Weak forms of the {E}hrenpreis conjecture and the surface subgroup conjecture},
      arxiv = {math/0411662},
      }
  • [calegari] Go to document D. Calegari, "Faces of the scl norm ball," Geom. Topol., vol. 13, iss. 3, pp. 1313-1336, 2009.
    @article{calegari, mrkey = {2496047},
      author = {Calegari, Danny},
      title = {Faces of the scl norm ball},
      journal = {Geom. Topol.},
      fjournal = {Geometry \& Topology},
      volume = {13},
      year = {2009},
      number = {3},
      pages = {1313--1336},
      issn = {1465-3060},
      mrclass = {20F65 (20F67 55N35 57M07)},
      mrnumber = {2496047},
      mrreviewer = {Patrick Bahls},
      doi = {10.2140/gt.2009.13.1313},
      zblnumber = {1228.20032},
      }
  • [e-m] Go to document A. Eskin and C. McMullen, "Mixing, counting, and equidistribution in Lie groups," Duke Math. J., vol. 71, iss. 1, pp. 181-209, 1993.
    @article{e-m, mrkey = {1230290},
      author = {Eskin, Alex and McMullen, Curt},
      title = {Mixing, counting, and equidistribution in {L}ie groups},
      journal = {Duke Math. J.},
      fjournal = {Duke Mathematical Journal},
      volume = {71},
      year = {1993},
      number = {1},
      pages = {181--209},
      issn = {0012-7094},
      coden = {DUMJAO},
      mrclass = {22E40 (57S30 58F17)},
      mrnumber = {1230290},
      mrreviewer = {Nimish A. Shah},
      doi = {10.1215/S0012-7094-93-07108-6},
      zblnumber = {0798.11025},
      }
  • [kahn-markovic-1] Go to document J. Kahn and V. Markovic, "Immersing almost geodesic surfaces in a closed hyperbolic three manifold," Ann. of Math., vol. 175, iss. 3, pp. 1127-1190, 2012.
    @article{kahn-markovic-1, mrkey = {2912704},
      author = {Kahn, Jeremy and Markovic, Vladimir},
      title = {Immersing almost geodesic surfaces in a closed hyperbolic three manifold},
      journal = {Ann. of Math.},
      fjournal = {Annals of Mathematics. Second Series},
      volume = {175},
      year = {2012},
      number = {3},
      pages = {1127--1190},
      issn = {0003-486X},
      coden = {ANMAAH},
      mrclass = {57M50 (30F40)},
      mrnumber = {2912704},
      mrreviewer = {James W. Anderson},
      doi = {10.4007/annals.2012.175.3.4},
      zblnumber = {06051269},
      }
  • [margulis] G. A. Margulis, "Certain applications of ergodic theory to the investigation of manifolds of negative curvature," Funkcional. Anal. i Priložen., vol. 3, iss. 4, pp. 89-90, 1969.
    @article{margulis, mrkey = {0257933},
      author = {Margulis, G. A.},
      title = {Certain applications of ergodic theory to the investigation of manifolds of negative curvature},
      journal = {Funkcional. Anal. i Priložen.},
      fjournal = {Akademija Nauk SSSR. Funkcional\cprime nyi Analiz i ego Priloženija},
      volume = {3},
      year = {1969},
      number = {4},
      pages = {89--90},
      issn = {0374-1990},
      mrclass = {53.72 (22.00)},
      mrnumber = {0257933},
      mrreviewer = {L. W. Green},
      zblnumber = {0207.20305},
     }
  • [p-p] J. Parkkonen and F. Paulin, Counting arcs in negative curvature.
    @misc{p-p,
      author = {Parkkonen, J. and Paulin, F.},
      title = {Counting arcs in negative curvature},
      arxiv = {1203.0175},
      }

Authors

Jeremy Kahn

CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016

Vladimir Markovic

Department of Mathematics, California Institute of Technology, Pasadena, CA 91125