TY - JOUR
T1 - The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary
AU - Huang, Rung Tzung
AU - Lee, Yoonweon
N1 - Funding Information:
The first author was supported partially by the National Science Council, Republic of China under the grant numbers NSC 100-2115-M-008-010-MY2 and NSC 102-2115-M-008-005 . The second author was supported by the National Research Foundation of Korea with the grant number NRF-2012R1A1A2001086 .
PY - 2014
Y1 - 2014
N2 - The refined analytic torsion on compact Riemannian manifolds with boundary has been discussed by B. Vertman (Vertman, 2009, 2008) and the authors (Huang and Lee, 2010, 2012) but these two constructions are completely different. Vertman used a double of de Rham complexes consisting of the minimal and maximal closed extensions of a flat connection and the authors used well-posed boundary conditions P-,L0, P+,L1 for the odd signature operator. In this paper we compare these two constructions by using the BFK-gluing formula for zeta-determinants, the adiabatic method for stretching cylinder part near boundary and the result for comparison of eta invariants inHuang and Lee (2012) when the odd signature operator comes from a Hermitian flat connection.
AB - The refined analytic torsion on compact Riemannian manifolds with boundary has been discussed by B. Vertman (Vertman, 2009, 2008) and the authors (Huang and Lee, 2010, 2012) but these two constructions are completely different. Vertman used a double of de Rham complexes consisting of the minimal and maximal closed extensions of a flat connection and the authors used well-posed boundary conditions P-,L0, P+,L1 for the odd signature operator. In this paper we compare these two constructions by using the BFK-gluing formula for zeta-determinants, the adiabatic method for stretching cylinder part near boundary and the result for comparison of eta invariants inHuang and Lee (2012) when the odd signature operator comes from a Hermitian flat connection.
KW - Eta-invariant
KW - Odd signature operator
KW - Primary
KW - Refined analytic torsion
KW - Secondary
KW - Well-posed boundary condition
KW - Zeta-determinant
UR - http://www.scopus.com/inward/record.url?scp=84887350789&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2013.10.015
DO - 10.1016/j.geomphys.2013.10.015
M3 - 期刊論文
AN - SCOPUS:84887350789
SN - 0393-0440
VL - 76
SP - 79
EP - 96
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -