Local index theorem for orbifold Riemann surfaces

DOI10.1007/s11005-018-01144-wzbMath1417.58024arXiv1701.00771OpenAlexW3105161350MaRDI QIDQ2000935

L. A. Takhtadzhyan, Peter Zograf

Publication date: 1 July 2019

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.00771

zbMATH Keywords

Fuchsian groupslocal index theoremsdeterminant line bundlesQuillen's metric

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Index theory and related fixed-point theorems on manifolds (58J20) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Determinants and determinant bundles, analytic torsion (58J52)

Related Items (9)

Determinant of Friedrichs Dirichlet Laplacians on 2-dimensional hyperbolic cones ⋮ Liouville action and holography on quasi-Fuchsian deformation spaces ⋮ Determinants of Laplacians for constant curvature metrics with three conical singularities on the 2-sphere ⋮ Analytic torsion for surfaces with cusps. I: Compact perturbation theorem and anomaly formula ⋮ Semiclassical 3D gravity as an average of large-\(c\) CFTs ⋮ Riemann-Roch isometries in the non-compact orbifold setting ⋮ Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities ⋮ Resolvent trace formula and determinants of \(n\) Laplacians on orbifold Riemann surfaces ⋮ Ruelle zeta function for cofinite hyperbolic Riemann surfaces with ramification points

Cites Work

• Unnamed Item
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• Unnamed Item
• Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces
• Algebraic geometry and the geometry of quantum strings
• Determinant fiber bundles, Quillen metric and degeneracy of curves.
• Cusps and the family hyperbolic metric
• Chern forms and the Riemann tensor for the moduli space of curves
• On determinants of Laplacians on Riemann surfaces
• Determinants of Cauchy-Riemann operators on a Riemann surface
• Determinants of Laplacians
• Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
• Riemann-Roch isometries in the non-compact orbifold setting
• A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces
• Some remarks on Teichmüller's space of Riemann surfaces
• Deformations and moduli of Riemann Surfaces with nodes and signatures.
• Fourier coefficients of the resolvent for a Fuchsian group.
• Central charge from adiabatic transport of cusp singularities in the quantum Hall effect

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