Higher-Rank Orthogonal Twists, APS Boundary Conditions, and -Equivariant Spectral Flow on a Warped Cylinder
This paper derives an explicit blockwise formula for the $RO(O(2))$-valued spectral flow of Dirac operators on a finite warped cylinder with higher-rank orthogonal twists and APS boundary conditions, demonstrating how representation-theoretic information is preserved beyond standard integer-valued spectral flow through the decomposition of moving and stationary blocks under reflection symmetry.