Real elements in the mapping class group of $T^2$

Details Real elements in the mapping class group of $T^2$ Real elements in the mapping class group of $T^2$

2010-06-03

arxiv.org/abs/1006.0752v2

Mathematics

Geometric Topology

15 pages, 11 figures

Scientific paper

10.1016/j.topol.2010.06.012

We present a complete classification of elements in the mapping class group of the torus which have a representative that can be written as a product of two orientation reversing involutions. Our interest in such decompositions is motivated by features of the monodromy maps of real fibrations. We employ the property that the mapping class group of the torus is identifiable with $SL(2,\Z)$ as well as that the quotient group $PSL(2,\Z)$ is the symmetry group of the {\em Farey tessellation} of the Poincar\'e disk.

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