Connected components of the Hurwitz space for the symmetric group of degree 7

Abstract EN

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.