Uniqueness of Maximal Curve Systems on Punctured Projective Planes | Synapse
October 8, 2025Open Access
Uniqueness of Maximal Curve Systems on Punctured Projective Planes
Key Points
Unique maximal 1-systems exist in punctured projective planes with up to five punctures.
The uniqueness of these systems hinges on the action of the mapping class group.
Understanding loops in these planes reveals important geometrical properties.
Investigation contributes to the broader field of topology and geometric structures.
Abstract
We show that the maximal 1-system of loops in a punctured projective plane is unique up to the mapping class group action if and only if the number of punctures is at most five.