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27 de julio de 2024
Asymptotic windings over the trefoil knot.
| Título inglés | Asymptotic windings over the trefoil knot. |
|---|---|
| Título español | Giros asintóticos sobre el nudo de trébol. |
| Autor/es | Franchi, Jacques |
| Organización | Univ. Louis Pasteur IRMA-CNRS, Estrasburgo, Francia |
| Revista | 0213-2230 |
| Publicación | 2005, 21 (3): 729-770, 20 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms. Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which is the asymptotic homology performed by the Brownian motion in G/Γ', describing thereby in an intrinsic way part of the asymptotic Brownian behavior in the fundamental group of the complement of the trefoil knot. A good basis of the cohomology of G/Γ', made of harmonic 1-forms, is calculated, and then the asymptotic Brownian behavior is obtained, by means of the joint asymptotic law of the integrals of the above basis along the Brownian paths. Finally the geodesics of G are determined, a natural class of ergodic measures for the geodesic flow is exhibited, and the asymptotic geodesic behavior in G/Γ' is calculated, by reduction to its Brownian analogue, though it is not precisely the same (counter to the hyperbolic case). |
| Clasificación UNESCO | 120212 |
| Palabras clave español | Nudos topológicos ; Movimiento browniano |
| Código MathReviews | MR2231009 |
| Código Z-Math | Zbl 1115.58029 |
 Acceso al artículo completo |
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