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" Proceedings of the Second ISAAC Congress "
edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara.
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BL
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| Record Number
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574264
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b403483
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| Main Entry
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Begehr, Heinrich G. W.
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| Title & Author
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Proceedings of the Second ISAAC Congress : Volume 2: This project has been executed with Grant No. 11-56 from the Commemorative Association for the Japan World Exposition (1970) /\ edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara.
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| Publication Statement
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Boston, MA :: Springer US,, 2000.
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| Series Statement
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International Society for Analysis, Applications and Computation,; 8
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| ISBN
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9781461302711
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: 9781461379713
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| Abstract
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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 ,1>2= 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)).
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Mathematics.
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Functional analysis.
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Functions of complex variables.
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Integral equations.
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Differential equations, Partial.
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Gilbert, Robert P.
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Kajiwara, Joji.
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SpringerLink (Online service)
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