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Summer 2014 The gluing formula of the zeta-determinants of Dirac Laplacians for certain boundary conditions
Rung-Tzung Huang, Yoonweon Lee
Illinois J. Math. 58(2): 537-560 (Summer 2014). DOI: 10.1215/ijm/1436275497

Abstract

The odd signature operator is a Dirac operator which acts on the space of differential forms of all degrees and whose square is the usual Laplacian. We extend the result see ( J. Geom. Phys. 57 (2007) 1951–1976) to prove the gluing formula of the zeta-determinants of Laplacians acting on differential forms of all degrees with respect to the boundary conditions $\mathcal{P}_{-,\mathcal{L}_{0}}$, $\mathcal{P}_{+,\mathcal{L}_{1}}$. We next consider a double of de Rham complexes consisting of differential forms of all degrees with the absolute and relative boundary conditions. Using a similar method, we prove the gluing formula of the zeta-determinants of Laplacians acting on differential forms of all degrees with respect to the absolute and relative boundary conditions.

Citation

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Rung-Tzung Huang. Yoonweon Lee. "The gluing formula of the zeta-determinants of Dirac Laplacians for certain boundary conditions." Illinois J. Math. 58 (2) 537 - 560, Summer 2014. https://doi.org/10.1215/ijm/1436275497

Information

Received: 23 April 2014; Revised: 9 August 2014; Published: Summer 2014
First available in Project Euclid: 7 July 2015

zbMATH: 06475312
MathSciNet: MR3367662
Digital Object Identifier: 10.1215/ijm/1436275497

Subjects:
Primary: 58J52
Secondary: 58J28, 58J50

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign

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Vol.58 • No. 2 • Summer 2014
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