Complex projective towers and their cohomological rigidity up to dimension six

A complex projective tower, or simply a $\mathbb C\mathrm P$-tower, is an iterated complex projective fibration starting from a point. In this paper we classify all six-dimensional $\mathbb C\mathrm P$-towers up to diffeomorphism, and as a consequence we show that all such manifolds are cohomologically rigid, i.e., they are completely determined up to diffeomorphism by their cohomology rings.