arXiv research

The paper proves a quadratic formality for Sasakian manifolds' representation varieties.

We provide models that are as close as possible to being formal for a large class of compact manifolds that admit a transversely Kaehler structure, including Vaisman and quasi-Sasakian manifolds. As an application we are able to classify the corresponding nilmanifolds.

We study a cohomology theory $H^{\bullet}_{\varphi}$, called the $\mathcal L_B$-cohomology, on compact torsion-free $\mathrm{G}_2$-manifolds. We show that $H^k_{\varphi} \cong H^k_{\mathrm{dR}}$ for $k \neq 3, 4$, but that $H^k_{\varphi}$ is infinite-dimensional for $k = 3,4$. Nevertheless there is a canonical injectio…

In this paper we introduce the notion of Poincaré DGCAs of Hodge type, which is a subclass of Poincaré DGCAs encompassing the de Rham algebras of closed orientable manifolds. Then we introduce the notion of the small algebra and the small quotient algebra of a Poincaré DGCA of Hodge type. Using these concepts, we inves…