A note on the homotopy invariance of Pontrjagin classes (Q1916451)

The following theorem is proved in this article: Let \(p\) be an odd prime. For every \(n \geq 1\), \(p_n \bmod p^r\) is homotopy invariant iff \(p = 3\) and \(r = 1\). This result develops the classical result of \textit{Wen-Tsün Wu} [Sci. Sinica 3, 353-367 (1954), 455-490 (1955; Zbl 0068.37005)] and excludes other Pontryagin classes of stable vector bundles with properties \(p \neq 3\) and \(r > 1\). The proof of the theorem is based on the Adams operation and on approaches of B. L. Sharma and W. T. Wu.