SOME INDEX FORMULAE ON THE MODULI SPACE OF STABLE PARABOLIC VECTOR BUNDLES

Pierre Albin, Frédéric Rochon

Type: Article

Publication Date: 2013-02-01

Citations: 9

DOI: https://doi.org/10.1017/s144678871200047x

Abstract

Abstract We study natural families of $\bar {\partial } $ -operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulae for the Chern classes of the associated determinant bundles consistent with a result of Takhtajan and Zograf.

Locations

Journal of the Australian Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (38)

Action	Title	Year	Authors
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+	A local index theorem for families of $$\bar \partial $$ -operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaceson punctured Riemann surfaces and a new Kähler metric on their moduli spaces	1991	Leon A. Takhtajan Peter Zograf
+ PDF Chat	Families of Dirac operators, boundaries and the $b$-calculus	1997	Richard Melrose Paolo Piazza
+	Erratum: ``Determinants of Laplacians on surfaces of finite volume''	1991	Isaac Efrat
+	Pseudodifferential operators, corners and singular limits	1990	Richard Melrose
+ PDF Chat	A new proof of a theorem of Narasimhan and Seshadri	1983	Simon Donaldson
+	Index and Spectral Theory for Manifolds with Generalized Fibred Cusps	2001	Boris Vaillant
+	Basics of the b-Calculus	2001	Daniel Grieser
+	Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature	1987	Rafe Mazzeo Richard Melrose
+ PDF Chat	Resolvent of the Laplacian on strictly pseudoconvex domains	1991	Charles L. Epstein Richard Melrose Gerardo A. Mendoza