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All figures (12)
Figure 13: The intersection of F0 with IC0 \ I 0 . The disc D0 is the interior of c0 D cC0 \ c 0 . The two segments cC 0 and c 0 are the thicker parts of F0\ IC0 and F0\ I 0 .
Figure 14: A combinatorial picture of the intersection of @D with DA . The top and bottom lines are identified. The curve c0 corresponds to the righthand side of the figure.
Figure 5: Vertical projections of the isometric spheres I˙ k for small values of k at the point .˛1; ˛2/D .0:4; 0:3/
Figure 3: Action of S and T on the tetrahedron .pA;pB;pAB;pBA/
Figure 2: The Whitehead link
Figure 11: Vertical projection and realistic view of the isometric spheres and the fans F0 and F 1 for the parameter values ˛1 D 0 , ˛2 D ˛lim2 . Compare with Figure 5.
Figure 7: Intersections of the isometric spheres I 0 , I 1 , IC 1 and IC 1 with IC0 in the boundary of H 2 C , viewed in geographical coordinates. Recall that rC 0 D IC 0 \ I 0 and r 0 D IC 0 \ I 1 . Here ˛ 2 2 ; 2 is the vertical coordinate, and ˇ 2 Œ ; the horizontal one. The vertical dash-dotted segments ˇ D ˙ 2 are the two halves of the boundary of the meridian m . The bigon between the two curves rC 0 and r 0 is BC 0 (see Proposition 6.5). Compare to [8, Figure 2].
Figure 4: The parameter space, with the parabolicity curve P and the regions E and L . The region Z is the central region, which is contained in the rectangle R .
Figure 6: Two realistic views of the isometric spheres IC0 , I C 1 and I 0 for the limit group lim . The thin bigon is BC 0 (defined in Proposition 6.5). Compare with Figures 7 and 12
Figure 10: The null locus of D.x;y/ in the rectangle Œ3; 4 3 2 ; 4
Figure 12: The intersection of F0 with IC0 drawn on I C 0 in geographical coordinates
Figure 1: The parameter space for U . The exterior curve P corresponds to classes of groups for which ŒA;B is parabolic. The central dashed curve bounds the region Z where we prove discreteness. The labels correspond to various special values of the parameters. Points with the same labels are obtained from one another by symmetries about the coordinate axes. The results of Section 3.3 imply that they correspond to groups conjugate in Isom(H 2C ).
Journal Article
•
DOI
•
A complex hyperbolic Riley slice
[...]
John R. Parker
1
,
Pierre Will
2
•
Institutions (2)
Durham University
1
,
University of Grenoble
2
06 Oct 2015
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arXiv: Geometric Topology