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Item Details
| Title:
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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) |
| By: |
H. Begehr (Editor), Robert P. Gilbert (Editor), Joji Kajiwara (Editor) |
| Format: |
Paperback |
| List price:
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£305.50 |
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We currently do not stock this item, please contact the publisher directly for
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| ISBN 10: |
1461379717 |
| ISBN 13: |
9781461379713 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
15 September, 2011 |
| Edition: |
Softcover reprint of the original 1st ed. 2000 |
| Series: |
International Society for Analysis, Applications and Computation 8 |
| Pages: |
821 |
| Synopsis: |
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)). |
| Illustrations: |
XIV, 821 p. |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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