Zero-Modes, Covariant Anomaly Counterparts and Reducible Connections in   Topological Yang-Mills Theory
  We introduce the covariant forms for the non-Abelian anomaly counterparts in topological Yang-Mills theory, which satisfies the topological descent equation modulo terms that vanish at the space of BRST fixed points. We use the covariant anomalies as a new set of observables, which can absorb both $\dw$ and $\db$ ghost number violations of zero-modes. Then, we study some problems due to the zero-modes originated from the reducible connections. 
Jae-Suk Park