Universal Bundle, Generalized Russian Formula and Non-Abelian Anomaly in Topological Yang-Mills Theory

Abstract

We re-examine the geometry and algebraic structure of BRST's of Topological Yang-Mills theory based on the universal bundle formalism of Atiyah and Singer. This enables us to find a natural generalization of the {\it Russian formula and descent equations\/}, which can be used as algebraic method to find the non-Abelian anomalies counterparts in Topological Yang-Mills theory. We suggest that the presence of the non-Abelian anomaly obstructs the proper definition of Donaldson's invariants.Comment: 16 pages, harvmac TeX, ESENAT-92-07, (TeXnical and stupid errors are corrected.