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Planar boundaries and parabolic subgroups
We study the Bowditch boundaries of relatively hyperbolic group pairs, focusing on the case where there are no cut points. We show that if (G,P) is a rigid relatively hyperbolic group pair whose boundary embeds in S2, then the action on the boundary extends to a convergence group action on S2. More generally, if the boundary is connected and planar with no cut points, we show that every element of P is virtually a surface group. This conclusion is consistent with the conjecture that such a group G is virtually Kleinian. We give numerous examples to show the necessity of our assumptions
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- Award ID(s):
- 2005353
- PAR ID:
- 10554953
- Publisher / Repository:
- Mathematical Research Letters
- Date Published:
- Journal Name:
- Math. Res. Lett.
- ISSN:
- 1073-2780
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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