Gauge groups and characteristic classes (Q1364157)

Given two vector bundles of the same finite rank over the same base space, the authors call them fundamentally equivalent (briefly: f-equivalent) if the gauge groups of the corresponding principal bundles are conjugate. Starting from a lemma asserting that two vector bundles are f-equivalent if and only if they are obtained from one another by tensoring with a line bundle, they intend to give a survey of topological properties of f-equivalent vector bundles. For instance, they present several claims comparing characteristic classes of f-equivalent vector bundles, or claims on relations between equivalence, f-equivalence, and stable equivalence. There are several incorrect claims or considerations. For example, in the statement of Theorem 14 the authors assume that \(rc_1(l) \neq 0\), but then in the ``proof'' they wish to convince the reader that \(rc_1(l)=0\).