Geography of non-formal symplectic and contact manifolds

TL;DR

This paper demonstrates the existence of symplectic and contact manifolds with specific Betti numbers, based on the non-formality of certain even- or odd-dimensional manifolds, expanding understanding of their geometric structures.

Contribution

It establishes a link between non-formal manifolds and the existence of symplectic or contact structures with prescribed Betti numbers, for various dimensions and Betti number conditions.

Findings

Existence of symplectic manifolds with given Betti numbers for even dimensions.

Existence of contact manifolds with given Betti numbers for odd dimensions.

Construction methods for manifolds with specified properties.

Abstract

Let (m,b) a pair of natural numbers. For m even (resp. m odd and b greater than or equal to 2) we show that if there is an m-dimensional non-formal compact oriented manifold whose first Betti number equals b, there is also a symplectic (resp. contact) manifold with these properties.