15 research outputs found
The braided Ptolemy-Thompson group is asynchronously combable
The braided Ptolemy-Thompson group is an extension of the Thompson
group by the full braid group on infinitely many strands. This
group is a simplified version of the acyclic extension considered by Greenberg
and Sergiescu, and can be viewed as a mapping class group of a certain infinite
planar surface. In a previous paper we showed that is finitely presented.
Our main result here is that (and ) is asynchronously combable. The
method of proof is inspired by Lee Mosher's proof of automaticity of mapping
class groups.Comment: 45
Asymptotically rigid mapping class groups and Thompson's groups
We consider Thompson's groups from the perspective of mapping class groups of
surfaces of infinite type. This point of view leads us to the braided Thompson
groups, which are extensions of Thompson's groups by infinite (spherical) braid
groups. We will outline the main features of these groups and some applications
to the quantization of Teichm\"uller spaces. The chapter provides an
introduction to the subject with an emphasis on some of the authors results.Comment: survey 77
The braided Ptolemy-Thompson group is finitely presented
Pursueing our investigations on the relations between Thompson groups and
mapping class groups, we introduce the group (and its further
generalizations) which is an extension of the Ptolemy-Thompson group by
means of the full braid group on infinitely many strands. We prove
that it is a finitely presented group with solvable word problem, and give an
explicit presentation of it.Comment: 35
An infinite genus mapping class group and stable cohomology
We exhibit a finitely generated group \M whose rational homology is
isomorphic to the rational stable homology of the mapping class group. It is
defined as a mapping class group associated to a surface \su of infinite
genus, and contains all the pure mapping class groups of compact surfaces of
genus with boundary components, for any and . We
construct a representation of \M into the restricted symplectic group of the real Hilbert space generated by the homology
classes of non-separating circles on \su, which generalizes the classical
symplectic representation of the mapping class groups. Moreover, we show that
the first universal Chern class in H^2(\M,\Z) is the pull-back of the
Pressley-Segal class on the restricted linear group
via the inclusion .Comment: 14p., 8 figures, to appear in Commun.Math.Phy