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 (the good pants are pairs of pants whose cuffs have the length nearly equal to some large number R). Combined with our previous work on the Surface Subgroup Theorem, this yields a proof of the Ehrenpreis conjecture.

Revised to incorporate the advice of the referee. Appendix 2 has been substantially rewritten. 78 pages

References in corpus (2)

• Weak Forms of the Ehrenpreis Conjecture and the Surface Subgroup Conjecture
• Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces

Cited by in corpus (5)

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• Incompressible surfaces in rank one locally symmetric spaces
• Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic 3-manifolds
• The Moduli space of Riemann Surfaces of Large Genus
• Integral Foliated Simplicial Volume of Aspherical Manifolds