English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The problem of existence of nontrivial Massey products in cohomology of aspace is well-known in algebraic topology and homological algebra. A number ofproblems in complex geometry, symplectic geometry, and algebraic topology canbe stated in terms of Massey products. One of such problems is to establishformality of smooth manifolds in rational homotopy theory. There have alreadybeen constructed a few classes of spaces with nontrivial triple Massey productsin cohomology. Until now, very few examples of manifolds $M$ with nontrivialhigher Massey products in $H^*(M)$ were known. In this work we introduce asequence of smooth closed manifolds $\{M_{k}\}^{\infty}_{k=1}$ such that$M_{k}\hookrightarrow M_{k+1}$ is a submanifold and a retract of $M_{k+1}$ forany $k\geq 1$ and there exists a nontrivial Massey product$\langle\alpha_{1},\ldots,\alpha_{n}\rangle$ in $H^*(M_{k})$ for each $2\leqn\leq k$. The sequence $\{M_k\}^{\infty}_{k=1}$ is determined by a new familyof flag nestohedra $\mathcal P_{Mas}$. We give P.D.E. for the two-parametricgenerating series of $\mathcal P_{Mas}$.

Direct families of polytopes with nontrivial Massey products