Proceedings of the Second Isaac Congress: This Project Has Been Executed With Grant No. 11-56 from the Commemorative Association for the Japan World Exposition (1970) - Couverture souple

9781461379713: Proceedings of the Second Isaac Congress: This Project Has Been Executed With Grant No. 11-56 from the Commemorative Association for the Japan World Exposition (1970)

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ISBN 10 : 1461379717 ISBN 13 : 9781461379713

Editeur : Springer-Verlag New York Inc., 2011

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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,

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�diteur: Springer-Verlag New York Inc.
Date d'�dition: 2011
Langue: anglais
ISBN 10: 1461379717
ISBN 13: 9781461379713
Reliure: Broch�
Nombre de pages: 835
�diteur: Begehr Heinrich G.W., Gilbert R.P., Kajiwara Joji
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Proceedings of the Second ISAAC Congress

Begehr, Heinrich G.W.|Gilbert, R. P.|Kajiwara, Joji

Edit� par Springer US, 2011

ISBN 10 : 1461379717 ISBN 13 : 9781461379713

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Volume 1: Preface. 1. A central limit theorem for the Simple random walk on a crystal lattice M. Kotani, T. Sunada. 2. Level Statistics for Quantum Hamiltonians - Some Preliminary Ideas toward Mathematical Justification of the Theory of Berry and Tabor. N� de r�f. du vendeur 4196084

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Proceedings of the Second ISAAC Congress

Heinrich G. W. Begehr

Edit� par Springer US Sep 2011, 2011

ISBN 10 : 1461379717 ISBN 13 : 9781461379713

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Taschenbuch. Etat : 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)). 840 pp. Englisch. N� de r�f. du vendeur 9781461379713

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Proceedings of the Second ISAAC Congress

Heinrich G. W. Begehr

Edit� par Springer US, Springer New York Sep 2011, 2011

ISBN 10 : 1461379717 ISBN 13 : 9781461379713

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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. 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 ,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)).Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 840 pp. Englisch. N� de r�f. du vendeur 9781461379713

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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)

Heinrich G. W. Begehr

Edit� par Springer US, 2011

ISBN 10 : 1461379717 ISBN 13 : 9781461379713

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Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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)). N� de r�f. du vendeur 9781461379713

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