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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Proceedings of the Second Isaac Congress: Volume 2: This Project Has Been Executed with Grant No. 11-56 from the Commemorative Association for the Jap

Proceedings of the Second Isaac Congress: Volume 2: This Project Has Been Executed with Grant No. 11-56 from the Commemorative Association for the Jap

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

Hardcover

Series: International Society for Analysis, Applications and Computa, Book 8

General Mathematics

ISBN10: 0792365984
ISBN13: 9780792365983
Publisher: Springer Nature
Published: Dec 31 2000
Pages: 821
Weight: 2.96
Height: 1.75 Width: 6.14 Depth: 9.21
Language: English
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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