Share
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 (in English)
Begehr, Heinrich G. W. ; Gilbert, R. P. ; Kajiwara, Joji (Author)
·
Springer
· Paperback
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 (in English) - Begehr, Heinrich G. W. ; Gilbert, R. P. ; Kajiwara, Joji
$ 208.41
$ 219.99
You save: $ 11.58
Choose the list to add your product or create one New List
✓ Product added successfully to the Wishlist.
Go to My WishlistsIt will be shipped from our warehouse between
Tuesday, June 18 and
Wednesday, June 19.
You will receive it anywhere in United States between 1 and 3 business days after shipment.
Synopsis "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 (in 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,