ACTION OF R-FUCHSIAN GROUPS ON CP2

作者：Cano Angel^*; Parker John R; Seade Jose

来源：Asian Journal of Mathematics, 2016, 20(3): 449-474.

• Group representation
• Fuchsian group
• limit set
• complex projective space

We look at lattices in Iso(+) (H-R(2)), the group of orientation preserving isometries of the real hyperbolic plane. We study their geometry and dynamics when they act on CP2 via the natural embedding of SO+(2, 1) -> SU(2, 1) subset of SL(3, C). We use the Hermitian cross product in C-2,C-1 introduced by Bill Goldman, to determine the topology of the Kulkarni limit set A(Kul) of these lattices, and show that in all cases its complement Omega(Kul) has three connected components, each being a disc bundle over Ha. We get that Omega(Kul) coincides with the equicontinuity region for the action on CP2. Also, it is the largest set in CP2 where the action is properly discontinuous and it is a complete Kobayashi hyperbolic space. As a byproduct we get that these lattices provide the first known examples of discrete subgroups of SL(3, C) whose Kulkarni region of discontinuity in CP2 has exactly three connected components, a fact that does not appear in complex dimension 1 (where it is known that the region of discontinuity of a Kleinian group acting on CP1 has 0, 1, 2 or infinitely many connected components).

• 出版日期2016-7