標題: Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography
作者: Takhtajan, LA
Teo, LP
應用數學系
Department of Applied Mathematics
公開日期: 1-Aug-2003
摘要: We rigorously define the Liouville action functional for the finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that classical action - the critical value of the Liouville action functional, considered as a function on the quasi-Fuchsian deformation space, is an antiderivative of a 1-form given by the difference of Fuchsian and quasi-Fuchsian projective connections. This result can be considered as global quasi-Fuchsian reciprocity which implies McMullen's quasi-Fuchsian reciprocity. We prove that the classical action is a Kahler potential of the Weil-Petersson metric. We also prove that the Liouville action functional satisfies holography principle, i.e., it is a regularized limit of the hyperbolic volume of a 3-manifold associated with a quasi-Fuchsian group. We generalize these results to a large class of Kleinian groups including finitely generated, purely loxodromic Schottky and quasi-Fuchsian groups, and their free combinations.
URI: http://dx.doi.org/10.1007/s00220-003-0878-5
http://hdl.handle.net/11536/27669
ISSN: 0010-3616
DOI: 10.1007/s00220-003-0878-5
期刊: COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume: 239
Issue: 1-2
起始頁: 183
結束頁: 240
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