Geometric Intersection Numbers on a Four-punctured Sphere
نویسنده
چکیده
Let G4 be the space of all simple closed geodesics on the punctured sphere Σ4. We construct an explicit homeomorphism of the completion of G4 onto a circle by using geometric intersection numbers. Also, we relate these geometric intersection numbers to trace polynomials of transformations corresponding to geodesics in G4 in a representation of π1(Σ4) into PSL(2,C).
منابع مشابه
Algebraic and Geometric Intersection Numbers for Free Groups
We show that the algebraic intersection number of Scott and Swarup for splittings of free groups coincides with the geometric intersection number for the sphere complex of the connected sum of copies of S × S.
متن کاملSelf-Intersection Numbers of Curves in the Doubly Punctured Plane
We address the problem of computing bounds for the self-intersection number (the minimum number of self-intersection points) of members of a free homotopy class of curves in the doubly-punctured plane as a function of their combinatorial length L; this is the number of letters required for a minimal description of the class in terms of a set of standard generators of the fundamental group, and ...
متن کاملSpiralling and Folding: The Topological View
For every n, we construct two arcs in the four-punctured sphere that have at least n intersections and which do not form spirals. This is accomplished in several steps: we first exhibit closed curves on the torus that do not form double spirals, then arcs on the four-punctured torus that do not form spirals, and finally arcs in the four-punctured sphere which do not form spirals.
متن کاملRigidity and Stability for Isometry Groups in Hyperbolic 4-Space
Rigidity and Stability for Isometry Groups in Hyperbolic 4-Space by Youngju Kim Advisor: Professor Ara Basmajian It is known that a geometrically finite Kleinian group is quasiconformally stable. We prove that this quasiconformal stability cannot be generalized in 4-dimensional hyperbolic space. This is due to the presence of screw parabolic isometries in dimension 4. These isometries are topol...
متن کاملGeometry of Loop Eisenstein Series
Part 3. Geometric Construction of Loop Eisenstein Series 31 11. Bloch’s Map 31 12. Adeleic Loop groups and G-bundles on a Punctured Surface 33 13. Affine flag varieties and extensions of G-bundles 38 14. Relative Chern classes and Central extensions 41 15. Loop Eisenstein Series and Geometric Generating Functions 47 16. Ribbons and a Formal Analogue 48 17. Example: Loop Eisenstein Series on P1. 53
متن کامل