2013/11/18 by Huang, Rung-Tzung, Lee, Yoonweon
#58J52 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1311.4281
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 of [15] 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 L0, \mathcal P_+, \mathcal L1. 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.