Communications in Analysis and Geometry

Volume 20 (2012)

Number 3

Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces

Pages: 455 – 499

DOI: http://dx.doi.org/10.4310/CAG.2012.v20.n3.a2

Author

Richard A. Wentworth (Department of Mathematics, University of Maryland, College Park)

Abstract

We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary satisfying local elliptic boundary conditions. The conditions are defined using the additional structure of a framing, or trivialization of the bundle near the boundary. An application to the computation of bosonization constants follows directly from these formulas.

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