Gardado en:
| Autor Principal: | |
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| Formato: | Recurso digital |
| Idioma: | inglés |
| Publicado: |
Zenodo
2026
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| Subjects: | |
| Acceso en liña: | https://doi.org/10.5281/zenodo.19738589 |
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Table of Contents:
- <p>We show that the cotangent bundle of Teichmüller space T (Σ_g) — Moncrief's reduced phase space for (2+1) vacuum gravity — arises by symplectic reduction of the zero-enstrophy coadjoint orbit of the corner symmetry group Diff(S) ⋉ SL(2,ℝ)^S by SDiff(S). The zero-enstrophy condition (vanishing normal bundle curvature K⊥) decouples the codimension-2 Codazzi equations, producing holomorphic quadratic differentials as the cotangent fiber. The Ricci equation forces the two normal-direction differentials to be real-proportional at all genera, by the open mapping theorem. The symplectic structure is verified via the Chern-Simons triangle: the corner symplectic potential, restricted to flat normal connections and reduced by SDiff, reproduces the canonical symplectic form on T up to the gravitational normalisation 1/(8πG). This connects the canonical reduction programme for (2+1) gravity with the coadjoint orbit classification of gravitational edge modes, identifying Moncrief's phase space as a distinguished orbit with maximally large little group.</p>