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

In 1980 J. Powell proposed that, for every genus $g$, five specific elementssuffice to generate the Goeritz group $\mathcal {G}_g$ of genus $g$ Heegaardsplittings of $S^3$. Powell's Conjecture remains undecided for $g \geq 4$. Let$\mathcal{P}_g \subset \mathcal {G}_g$ denote the subgroup generated byPowell's elements. Here we show that, for each genus $g$, the natural function$\mathcal {G}_g \to \mathcal {G}_{g+1}/\mathcal {P}_{g+1}$ is trivial.

Powell's Conjecture on the Goeritz group of $S^3$ is stably true