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On the gluing problem for Dirac operators on manifolds with cylindrical ends

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Abstract

Combining elements of the b-calculus and the theory of elliptic boundary value problems, we solve the gluing problem for b-determinants of Dirac type operators on manifolds with cylindrical ends. As a corollary of our proof, we derive a gluing formula for the b-eta invariant and also a relative invariant formula relating the b-spectral invariants on a manifold with cylindrical end to the spectral invariants with the augmented APS boundary condition on the corresponding compact manifold with boundary.

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Loya, P., Park, J. On the gluing problem for Dirac operators on manifolds with cylindrical ends. J Geom Anal 15, 285–319 (2005). https://doi.org/10.1007/BF02922197

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