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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Suppose $K$ is a knot in $S^3$ with bridge number $n$ and bridge distancegreater than $2n$. We show that there are at most ${2n\choose n}$ distinctminimal genus Heegaard splittings of $S^3\setminus\eta(K)$. These splittingscan be divided into two families. Two splittings from the same family becomeequivalent after at most one stabilization. If $K$ has bridge distance at least$4n$, then two splittings from different families become equivalent only after$n-1$ stabilizations. Further, we construct representatives of the isotopyclasses of the minimal tunnel systems for $K$ corresponding to these Heegaardsurfaces.

Stabilizing Heegaard Splittings of High-Distance Knots