Classification of complex projective towers up to dimension 8 and cohomological rigidity

Details Classification of complex projective towers up to dimension 8 and cohomological rigidity Classification of complex projective towers up to dimension 8 and cohomological rigidity

2012-03-20

arxiv.org/abs/1203.4403v2

Mathematics

Geometric Topology

27 pages, v2: Remark 2.8 removed

Scientific paper

A complex projective tower or simply a $\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\mathbb CP$-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. We also show that cohomological rigidity is not valid for 8-dimensional $\mathbb CP$-towers by classifying all $\mathbb CP^1$-fibrations over $\mathbb CP^3$ up to diffeomorphism. As a corollary we show that such $\mathbb CP$-towers are diffeomorphic if they are homotopy equivalent.

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