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Abstract
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Let
be a group generated by two positive multi-twists. We give some sufficient conditions
for
to be free or have no “unexpectedly reducible” elements. For a group
generated by two Dehn twists, we classify the elements in
which
are multi-twists. As a consequence we are able to list all the lantern-like relations in
the mapping class groups. We classify groups generated by powers of two
Dehn twists which are free, or have no “unexpectedly reducible” elements.
In the end we pose similar problems for groups generated by powers of
twists
and give a partial result.
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Keywords
mapping class group, Dehn twist, multi-twist,
pseudo-Anosov, lantern relation
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Mathematical Subject Classification 2000
Primary: 57M07
Secondary: 20F38, 57N05
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Publication
Received: 12 June 2002
Revised: 8 November 2002
Accepted: 17 December 2002
Published: 27 December 2002
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