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In Huang and Lee (in The Refined Analytic Torsion and a Well-posed Boundary Condition for the Odd Signature Operator, ) introduced a pair of new de Rham complexes on a compact oriented Riemannian manifold with boundary by using a pair of global boundary conditions to discuss the refined analytic torsion on a compact manifold with boundary. In this paper we discuss the Lefschetz fixed point formula on these complexes with respect to a smooth map which is a local isometry on the boundary and has only simple fixed points. For this purpose we are going to use the heat kernel method for the Lefschetz fixed point formula.

Lefschetz fixed point formula on a compact Riemannian manifold with boundary for some boundary conditions