#### Document Type

Article

#### Publication Date

3-22-2018

#### Abstract

Let *S* be a Riemann surface and *G* a large subgroup of* Aut(S)* (*Aut(S)* may be unknown). We are particularly interested in regular *n*-gonal surfaces, i.e., the quotient surface *S/G* (and hence *S/Aut(S)*) has genus zero. For various *H *the ramification information of the branched coverings *S/K -> S/H* may be captured in a matrix. The ramification information, in particular strong branching, may be then be used in analyzing the structure of *Aut(S)*. The ramification information is conjugation invariant so the matrix's rows and columns may be indexed by conjugacy classes of subgroups. The only required information is a generating vector for the action of *G*, and the subgroup structure. The latter may be computed using Magma or GAP. The signatures and generating vectors of the subgroups are not required.

#### Recommended Citation

Broughton, Sean A., "Branching matrices for the automorphism group lattice of a Riemann surface" (2018). *Mathematical Sciences Technical Reports (MSTR)*. 167.

https://scholar.rose-hulman.edu/math_mstr/167

*script for computing orbit space of pairs*

rammatrix.mgm (5 kB)

*script for computing ramification matrices*

## Comments

MSTR 18-01