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- From there we’ll give consideration to contact 3-manifold principle, together with Legendrian knots, overtwistedness and the Thurston-Bennequin inequality, open guide decompositions.
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The concept of Lie teams and Lie algebras is a classical and well-established subject of arithmetic. The plan for this course is to give an introduction to the foundations of this theory, with emphasis on compact Lie teams and semi-simple Lie algebras. In the third part, we’ll see tips on how to use ergodic concept to depend things, as an example closed geodesics on a manifold of unfavorable curvature. In order to do that, we are going to prove that the geodesic circulate is ergodic, and we will introduce dynamical ζ-functions and the Ruelle transfer operator. By learning the spectral theory for such an operator we will show the prime orbit theorem, i.e. the analog of the prime number theorem for closed geodesics on a hyperbolic manifold.
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