Proceedings of the Second ISAAC Congress: Volume 2: This project has been executed with Grant No. 11-56 from the Commemorative Association for the ... for Analysis, Applications and Computation) - Tapa dura

Proceedings of the Second ISAAC Congress

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BuchWeltWeit Ludwig Meier e.K.
(Bergisch Gladbach, Alemania)

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Descripción Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Let 8 be a Riemann surface of analytically finite type (9, n) with 29 2+n O. Take two pointsP1, P2 E 8, and set 8 ,12= 8 {P1' P2}. Let PI Homeo+(8;P1,P2) be the group of all orientation preserving homeomor phismsw: 8 -+ 8 fixingP1, P2 and isotopic to the identity on 8. Denote byHomeot(8;Pb P2) the set of all elements ofHomeo+(8;P1, P2) iso topic to the identity on 8 ,P2' ThenHomeot(8;P1,P2) is a normal sub pl group ofHomeo+(8;P1,P2). We setIsot(8;P1,P2) =Homeo+(8;P1,P2)/ Homeot(8;p1, P2). The purpose of this note is to announce a result on the Nielsen Thurston-Bers type classification of an element [w] ofIsot+(8;P1,P2). We give a necessary and sufficient condition for thetypeto be hyperbolic. The condition is described in terms of properties of the pure braid [b ] w induced by [w]. Proofs will appear elsewhere. The problem considered in this note and the form ofthe solution are suggested by Kra's beautiful theorem in [6], where he treats self-maps of Riemann surfaces with one specified point. 2 TheclassificationduetoBers Let us recall the classification of elements of the mapping class group due to Bers (see Bers [1]). LetT(R) be the Teichmiiller space of a Riemann surfaceR, andMod(R) be the Teichmtiller modular group of R. Note that an orientation preserving homeomorphism w: R -+ R induces canonically an element (w) EMod(R). Denote by&.r(R)( ,.) the Teichmiiller distance onT(R). For an elementXEMod(R), we define a(x)= inf &.r(R)(r,x(r)). 196 pp. Englisch. Nº de ref. del artículo: 9780792365983

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