Webbtechniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. WebbWe show that the number of square-tiled surfaces of genus , with marked points, with one or both of its horizontal and vertical foliations belonging to fixed mapping class group …

Lecture 1. Count of simple closed geodesics on Riemann surfaces …

WebbTo any compact Riemann surface of genus one may assign a principally polarized abelian variety of dimension , the Jacobian of the Riemann surface. The Jacobian is a complex torus, and a Gram matrix of the lattice of a… Webbfor a hyperbolic 3-manifold M. Any φ∈ R+·Fdetermines a measured foliation F of M. Generaliz-ing the case of Teichmu¨ller geodesics and fibrations, we show F carries a canonical Riemann surface structure on its leaves, and a transverse Teichmu¨ller flow with pseudo-Anosov expansion factor K(φ) >1. We introduce a polynomial invariant Θ initialise a vector in c++

Non-simple closed geodesics on hyperbolic surfaces

Webb9 jan. 2024 · not contain any simple closed geodesics, as with the hyperbolic thrice-punctured sphere.However,amongtheorientable,finitearea,completehyperbolic2 … WebbCount of simple closed geodesics on Riemann surfaces (after Maryam Mirzakhani) Anton Zorich (Reference: M. Mirzakhani, “Growth of the number of simple closed geodesics on … Webbat torus all closed geodesics are simple and similarly, on a hyperbolic surface, the set of all closed geodesics is not only dense but also dense in the unit tangent bundle. This is one … initialise.bat initialise startup