Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces

Details Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces

2010-08-17

arxiv.org/abs/1008.2914v4

Mathematics

Differential Geometry

Final version; to appear in Communications in Analysis and Geometry

Scientific paper

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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