The MAPCLASS Package
- Adam James
- Kay Magaard
- Sergey Shpectorov
- Helmut Völklein
Description
MAPCLASS is a package for GAP used to compute and inspect mapping class orbits.What are mapping class orbits?
Suppose that \( G \) is a finite group, and \( \textbf{C} = ( C_1, \ldots, C_r ) \) is a sequence of conjugacy classes of \( G \), and let \(S_{g,r} \) denote the compact connected surface of genus \(g\) with \(r\) marked points. The MAPCLASS package for GAP computes all possible homomorphisms $$ \phi: \pi_1(S_{g,r}) \longrightarrow G $$ up to precomposition with the isomorphism \( \theta : \pi_1(S_{g,r}) \longrightarrow \pi_1(S_{g,r})\) induced by a member of the mapping class group \( \text{Mod}(S_{g,r})\). We call these equivalence classes mapping class orbits. For more information on these orbits, including a description of the BRAID package - a precursor to MAPCLASS - see the following references:
- K. Magaard, S. Shpectorov and H. Völklein. "A GAP package for braid orbit computation and applications"
- K. Magaard, T.Shaska, S. Shpectorov and H. Völklein. "The locus of curves with prescribed automorphism group"
- H. Völklein. "The image of a Hurwitz space under the moduli map"
Downloads
The package can be downloaded is the following formats:Documentation
The documentation can be viewed online here. The documentation can also be downloaded in the following other formats:License
The package is released under the GNU General Public License version 2 or later. Details of this license can be found here.Contact
Please send any bug reports, comments, or suggestions for improvements to one of the following maintainers:- Adam James ( jamesa@maths.bham.ac.uk )
- Kay Magaard ( k.magaard@maths.bham.ac.uk )
- Sergey Shpectorov ( s.shpectorov@bham.ac.uk )