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We interpret the Hilden subgroup of the mapping class group of
a surface in terms of motions of "wickets" in upper-half space and give
a finite presentation for this group. (Hilden previously gave a finite
generating set.) We will also use the wicket viewpoint to relate
Hilden's group to the so-called "ring-group," or the group of motions of
circles in 3-space. Further, we will discuss a K(pi,1)-space for the
wicket group as well as some related spaces among which we show certain
homotopy equivalences. This is joint work with Allen Hatcher.
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