The solution on the geography-problem of non-formal compact (almost) contact manifolds

TL;DR

This paper constructs specific non-formal compact (almost) contact manifolds with prescribed dimensions and Betti numbers, including simply-connected examples for certain parameters, addressing a key problem in contact topology.

Contribution

It provides explicit examples of non-formal contact manifolds with given Betti numbers, solving the geography problem for these manifolds in specified dimensions.

Findings

Existence of non-formal contact manifolds for odd dimensions m ≥ 7 with b₁=1.

Existence of non-formal contact manifolds for odd dimensions m ≥ 5 with b₁=0.

Construction of simply-connected examples when m ≥ 7 and b=0.

Abstract

Let $(m,b)$ be a pair of natural numbers. For $m$ odd with $m \ge 7$ (resp. $m \ge 5$) and $b=1$ (resp. $b=0$) we show that there is a non-formal compact (almost) contact $m$-manifold with first Betti number $b_1 = b$. Moreover, in the case $b = 0$ with $m \ge 7$, the manifold even is simply-connected.