CORDIS Archive : Training and Mobility of Researchers / Contract Nr : FMBICT972544

GEODESICS ON FLAT SURFACES WITH CONICAL SINGULARITIES / ZETA FUNCTION FOR AUTOMORPHISMS OF FREE GROUPS

Host Laboratory	Scientific Supervisor
Ruhr-Universität Bochum Institut für Mathematik - Fakultät für Mathematik UNIVERSITAET STRASSE 150 44780 Bochum Germany	Dr. Martin Lustig Tel : 49/2347003348 / Fax : 49/2347094531 Email : Martin.Lustig@rz.ruhr-uni-bochum.de
	Grant Holder
	Dr. Jean-Christophe Curtillet (French) Tel : 49/2349799097 / Fax : 49/2349799096 Email : jean.curtillet@ruhr-uni-bochum.de
Abstract 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) Contract number : FMBICT972544 Duration : 24 Months -- signed on 01-12-97 -- Category 30 (B30)

Last updated :10:07:98

Do you have questions or comments about this site : tmr-grants@dg12.cec.be