Dirichlet Ford domains Experiments and on manifolds dimensional hyperbolic for 3 cone - Hirotaka A Kiyoshi University ) ( Osaka City Workshop Topology and Computer 2017 ) ( Osaka University at Oct 21 2017 , .
Dirichlet Ford domains Experiments and on manifolds dimensional hyperbolic for 3 cone - Hirotaka A Kiyoshi University ) ( Osaka City A part with of talk " related " this is Yamashita Yasushi with joint project a Workshop Topology and Computer 2017 ) ( Osaka University at Oct 21 2017 , .
# EPSL Question When ( A discrete 17 , B > ( ) sic is = , e) ? of elements A BEPSL ( 2 for given pair a , ' 'C%±[ } ( 2 PSL E) SL ( 2 = a , = YET } ± > E { : E 14h ) 9 - 3 At I Isomt = H% M • P PSLC e) ←> 2. < ( orbifold ) " " # complete hyp manifold discrete M p : : a almost with , ( M ) IT it
Y @ Case , B ] [ A : known : is A algorithm practical parabolic [ A its ] parab BEPSL with INPUT e) A ( 2. , following OUTPUT of One the : ( Jorgensen theory ) discrete free and P @ is ) Leutbecher ( discrete Shimizu not D ' 17 is - for @€ Don't know 0 [ A. B) € B Quasifuchsian Background space punctured torus
31 @ Software Picture of Bers slice Wada OPTI M by a . Yamashita Produced by Yasushi with work based his joint on Y . Komori . Sagawa T & . Wada M ,
y @ Jorgensen Theory of comb of the characterization Str gives a . . for punctured torus the domains Ford groups . P III. Ford domain : * :¥iE÷EE⇐*€n¥I¥ lH3 for canonical P fund domain A a . he :# p=M-Ccnt_bc# x ) ⇒ at shortest least paths 2
Jorgensen Theory %L of variation A possible " puncture " " " point Change to cone Gec t.MY#i& to * - , R M To ZI ) M ( = × To R 0<0 × < = 7- natural of " → Ford extension domains " a
Jorgensen Theory %L of variation A possible " puncture " " " point Change to cone Ec c ' . YI.fiiG-tYI@ee.o :* R M To ZI ) M ( = × To R 0<0 × < = 7- natural of " → Ford extension domains " a CANONICAL ! ! BUT NOT
61 @ Problems pending horses < A , B > is " The " group � 1 � . image of hole the as repr . . not 01k€ discrete when Q horoballs . ' # ( canonical like lH3 ) universal � 1 � covering . " The " unique NOT � 2 � are .
61 @ Problems pending horses < A , B > is " The " group � 1 � . image of hole the as repr . . not 01h discrete when Et Q . horoballs ' # ( canonical like lH3 ) universal � 1 � covering . Some CATH argument using ) space → . " The " unique NOT � 2 � are . the family them Connect of → by ( Today 's domains Dirichlet . ) experiment .
%L Ford Dirichlet domains and in 9µg Ford Recall domain : = ) text ¥ Ct d " M-ccutbocusw.in#DefDirichletdomain=M-(cutloc=r.bap x i | base pt I ← × ← c- Thm a strongly If subset M then contains compact convex , } { comb of Dirichlet < # domains Str Ford & is . . .
%L Software A ) construction ( under angle fixed Cone is • . Can • move - hyperbolic structures Dirichlet domains for points base - of ) OPTI ( a early like Looks version very • Developed Swift Apple 's " with " • MacBook Pro and runs my on . Let's → see ... .
%L ( Yz ) mathematics Questions in - that : likely It • is " draw the software limit ' ' set If order to we , " the plane " will then draw it Jordan curve on a . ? What does it mean between Is any correspondence there • ' ' the the imaginary boundary plane ' ' and of ? reasonable a space
@ 14 ( 212 ) Questions in programing - the speed ? I How improve can My Software Cocoa ? " Kit " of " Scene uses ? " " time views produce real Can I - - only < 1000 hemispheres . The contains scene like Suggestions ← " l ' ' development another environment Use . welcome also is . Thank you
Recommend
More recommend