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Local index theorem for orbifold Riemann surfaces. / Takhtajan, L.A.; Zograf, Peter .

In: Letters in Mathematical Physics, Vol. 109, No. 5, 01.05.2019, p. 1119-1143.

Research output: Contribution to journal › Article › peer-review

Harvard

Takhtajan, LA & Zograf, P 2019, 'Local index theorem for orbifold Riemann surfaces', Letters in Mathematical Physics, vol. 109, no. 5, pp. 1119-1143. https://doi.org/10.1007/s11005-018-01144-w

APA

Takhtajan, L. A., & Zograf, P. (2019). Local index theorem for orbifold Riemann surfaces. Letters in Mathematical Physics, 109(5), 1119-1143. https://doi.org/10.1007/s11005-018-01144-w

Vancouver

Takhtajan LA, Zograf P. Local index theorem for orbifold Riemann surfaces. Letters in Mathematical Physics. 2019 May 1;109(5):1119-1143. https://doi.org/10.1007/s11005-018-01144-w

Author

Takhtajan, L.A. ; Zograf, Peter . / Local index theorem for orbifold Riemann surfaces. In: Letters in Mathematical Physics. 2019 ; Vol. 109, No. 5. pp. 1119-1143.

BibTeX

@article{884eda9b092c475b992c448cc8b9028d,
title = "Local index theorem for orbifold Riemann surfaces",
abstract = "We derive a local index theorem in Quillen{\textquoteright}s form for families of Cauchy–Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. Each conical point (or a conjugacy class of primitive elliptic elements in the Fuchsian group) gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new K{\"a}hler metric on the moduli space of Riemann orbisurfaces. We find a simple formula for a local K{\"a}hler potential of the elliptic metric and show that when the order of elliptic element becomes large, the elliptic metric converges to the cuspidal one corresponding to a puncture on the orbisurface (or a conjugacy class of primitive parabolic elements). We also give a simple example of a relation between the elliptic metric and special values of Selberg{\textquoteright}s zeta function.",
keywords = "Determinant line bundles, Fuchsian groups, Local index theorems, Quillen{\textquoteright}s metric, \ Fuchsian groups, Quillen's metric",
author = "L.A. Takhtajan and Peter Zograf",
year = "2019",
month = may,
day = "1",
doi = "10.1007/s11005-018-01144-w",
language = "English",
volume = "109",
pages = "1119--1143",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - Local index theorem for orbifold Riemann surfaces

AU - Takhtajan, L.A.

AU - Zograf, Peter

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We derive a local index theorem in Quillen’s form for families of Cauchy–Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. Each conical point (or a conjugacy class of primitive elliptic elements in the Fuchsian group) gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new Kähler metric on the moduli space of Riemann orbisurfaces. We find a simple formula for a local Kähler potential of the elliptic metric and show that when the order of elliptic element becomes large, the elliptic metric converges to the cuspidal one corresponding to a puncture on the orbisurface (or a conjugacy class of primitive parabolic elements). We also give a simple example of a relation between the elliptic metric and special values of Selberg’s zeta function.

AB - We derive a local index theorem in Quillen’s form for families of Cauchy–Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. Each conical point (or a conjugacy class of primitive elliptic elements in the Fuchsian group) gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new Kähler metric on the moduli space of Riemann orbisurfaces. We find a simple formula for a local Kähler potential of the elliptic metric and show that when the order of elliptic element becomes large, the elliptic metric converges to the cuspidal one corresponding to a puncture on the orbisurface (or a conjugacy class of primitive parabolic elements). We also give a simple example of a relation between the elliptic metric and special values of Selberg’s zeta function.

KW - Determinant line bundles

KW - Fuchsian groups

KW - Local index theorems

KW - Quillen’s metric

KW - \ Fuchsian groups

KW - Quillen's metric

UR - http://www.scopus.com/inward/record.url?scp=85058374048&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/local-index-theorem-orbifold-riemann-surfaces

U2 - 10.1007/s11005-018-01144-w

DO - 10.1007/s11005-018-01144-w

M3 - Article

VL - 109

SP - 1119

EP - 1143

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 5

ER -

ID: 41877343