Premium
Asymptotic Singular Homology of a Complete Hyperbolic 3‐Manifold of Finite Volume
Author(s) -
Franchi J.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599011971
Subject(s) - mathematics , geodesic , brownian motion , finite volume method , pure mathematics , totally geodesic , flow (mathematics) , mathematical analysis , manifold (fluid mechanics) , limit (mathematics) , homology (biology) , combinatorics , geometry , statistics , physics , mechanics , mechanical engineering , biochemistry , chemistry , engineering , gene
Let V be a complete connected hyperbolic 3‐manifold of finite volume, with Liouville measure m , geodesic flow Γ t and Brownian motion Z t . Let ω be a smooth 1‐form, closed in the cusps of V. Then the limit laws as t → ∞ of( t log t ) − 1 / 2∫ 0 t ω ( Γ s ) under m and of( t log t ) − 1 / 2∫ 0 t ω ( Z s ) are calculated, and seen to be Gaussian, and equal. The geodesic flow case is studied via the Brownian case. 1991 Mathematics Subject Classification : 60J65, 58F17, 51M10.