Intersection Form, Laminations and Currents on Free Groups
نویسندگان
چکیده
منابع مشابه
R-trees and laminations for free groups I: Algebraic laminations
This paper is the first of a sequence of three papers, where the concept of an Rtree dual to (the lift to the universal covering of) a measured geodesic lamination L in a hyperbolic surface S is generalized to arbitrary R-trees provided with a (very small) action of the free group FN of finite rank N ≥ 2 by isometries. In [CHL-II] to any such R-tree T a dual algebraic lamination L(T ) is associ...
متن کاملCurrents on Free Groups
We study the properties of geodesic currents on free groups, particularly the " intersection form " that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces .
متن کاملR-trees and laminations for free groups III: Currents and dual R-tree metrics
A geodesic lamination L on a closed hyperbolic surface S, when provided with a transverse measure μ, gives rise to a “dual R-tree” Tμ, together with an action of G = π1S on Tμ by isometries. A point of Tμ corresponds precisely to a leaf of the lift L̃ of L to the universal covering S̃ of S, or to a complementary component of L̃ in S̃. The G-action on T is induced by the G-action on S̃ as deck transf...
متن کاملar X iv : 0 71 1 . 43 37 v 2 [ m at h . G T ] 2 2 Fe b 20 09 INTERSECTION FORM , LAMINATIONS AND CURRENTS ON FREE GROUPS
Let F be a free group of rank N ≥ 2, let µ be a geodesic current on F and let T be an R-tree with a very small isometric action of F. We prove that the geometric intersection number T, µ is equal to zero if and only if the support of µ is contained in the dual algebraic lamination L 2 (T) of T. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectr...
متن کاملar X iv : 0 71 1 . 43 37 v 1 [ m at h . G T ] 2 7 N ov 2 00 7 INTERSECTION FORM , LAMINATIONS AND CURRENTS ON FREE GROUPS
Let F N be a free group of rank N ≥ 2, let µ be a geodesic current on F N and let T be an R-tree with a very small isometric action of F N. We prove that the geometric intersection number T, µ is equal to zero if and only if the support of µ is contained in the dual algebraic lamination L 2 (T) of T. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2009
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-009-0041-3