On Fibrations with Formal Elliptic Fibers

Abstract

We prove that for a fibration of simply-connected spaces of finite type F ↪→ E → B with F being positively elliptic and H∗(F,Q) not possessing non-trivial derivations of negative degree, the base B is formal if and only if the total space E is formal. Moreover, in this case the fibration map is a formal map. As a geometric application we show that positive quaternion Kähler manifolds are formal and so are their associated twistor fibration maps.

Cite this paper

@inproceedings{Amann2011OnFW, title={On Fibrations with Formal Elliptic Fibers}, author={Manuel Amann and VITALI KAPOVITCH}, year={2011} }