Non-ergodicity on the SU(2)-character varieties
Abstract
We describe the dynamics of a group generated by Dehn twists along two filling multi-curves or a family of filling curves on the SU(2)-representation variety of closed surfaces. Consequently, we provide explicit -invariant rational functions on the representation variety of the genus two closed surface S2 for some pair of multi-curves. We establish a similar result for the SU(2)-character variety of genus four non-orientable surfaces N4 for some family of filling curves.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.