  We present a polarization and topology resolved study of the low energy band
structure in optimally doped superconducting Ba0.6K0.4Fe2As2 using angle
resolved photoemission spectroscopy. Polarization-contrasted measurements allow
us to identify and trace all low energy bands expected in models, revealing
unexpected symmetry breaking and a surprisingly intertwined Fermi surface
topology of hole-like bands near the Brillouin zone center. Band structure
correlations across the Gamma-M spin fluctuation wavevector are compared with
the superconducting gap anisotropy which suggest a partial scenario for
spin-mediated interband instability contributing to superconductivity in the
hole doped regime.
