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arXiv · 1905.05671

Symplectic domination

Joel Fine·Dmitri Panov
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Abstract

Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem of Ontaneda that gives a Riemannian manifold N of tightly pinched negative curvature which admits a map to M of degree equal to one; the second is a result of Donaldson on the existence of symplectic divisors. Given Ontaneda's negatively curved manifold N, the twistor space Z is symplectic. The manifold S is then a suitable multisection of the twistor space, found via Donaldson's theorem.

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Joel Fine, Dmitri Panov. 2019-05-14. Symplectic domination. https://doi.org/10.1112/blms.12402

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