Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7

Haval M. Mohammed Salih


The Hurwitz space  is the space of genus  covers of the Riemann sphere  with branch points and the monodromy group . Let be the symmetric group . In this paper, we enumerate the connected components of . Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of . This work gives us the complete classification of  primitive genus zero symmetric group of degree seven.



Monodromy Groups; Braid Orbits; Connected Components.

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