Academic Journal
Exceptional orbits of the pure Mapping Class Group in the character variety.
| Τίτλος: | Exceptional orbits of the pure Mapping Class Group in the character variety. |
|---|---|
| Συγγραφείς: | Golsefidy, Alireza S1 (AUTHOR), Tamam, Nattalie2 (AUTHOR) |
| Πηγή: | IMRN: International Mathematics Research Notices. Aug2026, Vol. 2026 Issue 15, p1-32. 32p. |
| Θεματικοί όροι: | *Representations of groups (Algebra) |
| Περίληψη: | Our primary objective is to construct closed subschemes of the character variety of the two-holed torus and the twisted character variety of a genus- |$2$| surface that satisfy the following properties: (1) They are invariant under the action of the corresponding pure Mapping Class Groups (MCGs). (2) They contain characters arising from dense representations into |$\operatorname{SU}_{2}(\mathbb{C})$| and |$\operatorname{SL}_{2}(\mathbb{Z}_{p})$| for primes |$p> 5$|. (3) For any characteristic zero field |$F$| , and every absolutely irreducible character |$x$| in the |$F$| -points of these subschemes, the Zariski closure of the pure MCG orbit of |$x$| in the modified relative character variety has strictly smaller dimension. Our construction shows that [9, Theorem 1.4] is incorrect. In [5], we prove that these subschemes precisely characterize the locus of exceptional infinite orbits under the action of pure MCGs. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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