
TL;DR
This paper classifies all orientation-preserving actions of certain projective special linear groups on orientable surfaces by computing their signatures, linking group theory, topology, and algebraic geometry.
Contribution
It provides a complete classification of signatures for $PSL_2({7})$ and $PSL_2({11})$, connecting group actions with Galois theory and geometric structures.
Findings
Classified all signatures for $PSL_2({7})$ and $PSL_2({11})$
Linked group actions to the inverse Galois problem
Bridged topology, geometry, and algebra in the classification
Abstract
We compute all signatures of , and which classify all orientation preserving actions of the groups , and on compact, connected, orientable surfaces with orbifold genus . This classification is well-grounded in the other branches of Mathematics like topology, smooth, and conformal geometry, algebraic categories, and it is also directly related to the inverse Galois problem.
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