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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). Softcover reprint of the original 1st ed. 2000.
・ISBN 978-1-4613-7971-3 paper EUR 199.99
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| 著者・編者 | Begehr, Heinrich G.W. / Gilbert, R.P. / Kajiwara, Joji (eds.), |
|---|---|
| シリーズ | International Society for Analysis, Applications and Computation |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2011 |
| ページ数 | 821 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-17490＞ |
解説
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)).