  An interplay of an exotic quantum holonomy and exceptional points is examined
in one-dimensional Bose systems. The eigenenergy anholonomy, in which Hermitian
adiabatic cycle induces nontrivial change in eigenenergies, can be interpreted
as a manifestation of eigenenergy's Riemann surface structure, where the branch
points are identified as the exceptional points which are degeneracy points in
the complexified parameter space. It is also shown that the exceptional points
are the divergent points of the non-Abelian gauge connection for the gauge
theoretical formulation of the eigenspace anholonomy. This helps us to evaluate
anti-path-ordered exponentials of the gauge connection to obtain gauge
covariant quantities.
