Pullback functors for reduced and unreduced \(L^{q,p}\)-cohomology (Q2674963)

The author states that every uniform map can be approximated by a smooth map with uniformly bounded derivatives. Then he sets up the (un)reduced \(L^{p,q}\)-cohomology. Also, he introduces the fiber volume of a Lipschitz submersion. In the last section, he establishes a particular Thom form. Then, he proves the uniform homotopy invariance of the \(L^2\)-index of a suitable signature operator defined by \textit{F. Bei} [J. Topol. Anal. 8, No. 1, 151--186 (2016; Zbl 1404.58006)].