Reflection symmetry on twisted Dirac operators on warped cylinders holds precisely when 2A is integer, yielding unitary equivalence of APS blocks and an RO(O(2))-valued or mod-two spectral-flow invariant.
An Equivariant Atiyah–Patodi–Singer Index Theorem for Proper Actions I: The Index Formula
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Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylinder
Reflection symmetry on twisted Dirac operators on warped cylinders holds precisely when 2A is integer, yielding unitary equivalence of APS blocks and an RO(O(2))-valued or mod-two spectral-flow invariant.