On independent rigid classes in \(H^{\ast}(\text{WU}_{q})\) (Q2452320)

The paper inscribes into a long series of publications on the rigidity and linear independence of characteristic classes of foliations. The author turns the attention to transversely holomorphic foliations and their characteristic classes. Using the complexification of Baker's example, cf. [\textit{D. Baker}, Comment. Math. Helv. 53, 334--363 (1978; Zbl 0388.57014)], the author shows the linear independence of a certain family of rigid classes in \(H^*(WU_q)\) which, moreover, is different from the ones studied by \textit{S. Hurder} in [Invent. Math. 66, 313--323 (1982; Zbl 0489.57006)]. The construction makes it evident that some of these characteristic classes are products of rigid and variable classes.