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The picture in the upper half-space model of tex2html_wrap_inline1411

To describe how to cut up tex2html_wrap_inline1891 , it is convenient to use the upper half-space model for tex2html_wrap_inline1411 . In this model, we represent tex2html_wrap_inline1411 as the upper half-space

displaymath1951

outfitted with the metric

The sphere at infinity appears as the (x,y)-plane, together with a point tex2html_wrap_inline1965 at infinity.

In this model, which was already tacitly used in Figure 3, the circles tex2html_wrap_inline1429 appear as circles, possibly degenerating into straight lines, in the (x,y)-plane. The planes tex2html_wrap_inline1897 appear as hemispheres, possibly degenerating into planes, that are perpendicular to the (x,y)-plane.


Peter Doyle