Geodesics on flat surfaces with conical singularities / zeta function forautomorphisms of free groups
FP4 — Training and Mobility of Researchers
- Duration
- 1998-06-01 → 2000-05-31
- EU contribution
- —
- Participants
- 2
- Scheme
- RGI
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Project objective
Research objectives and content The project contains two parts which will be pursued simultaneously: A-Geodesics on flat surfaces with singular points B-Zeta function for free groups automorphisms. In my Ph.D. thesis A-l studied surfaces which are obtained by certain identification of the edges of regular 4g-gon. B-l introduced and computed a zeta function for a large class of free group automorphisms. Goals A1: Generalize the results of my thesis to more general flat surfaces with singularities. A2: Describe the geodesics on such surfaces which contain a singularity. A3: Compute or at least estimate the growth function of simple geodesics and of multiple points in dependence of the length A4: Computing the number, length and homotopy class of the systoles of such surfaces and compute Gromov's isosystolic inequalities. B1: Give an algebraic-dynamic zeta function for all automorphisms of free groups. B2: Extend the definition to automorphisms of surfaces and word-hyperbolic groups. B3: Compute efficiently this zeta function and prove ist rationality Training content (objective, benefit and expected impact) Publishing papers. Learning the geometric group theory with M. Lustig and the three dimensional topology with H. Zieschang. Links with industry / industrial relevance (22)
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