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

Motivated by the L-space conjecture, we investigate various notions oforder-detection of slopes on knot manifolds. These notions are designed tocharacterise when rational homology 3-spheres obtained by gluing compactmanifolds along torus boundary components have left-orderable fundamentalgroups and when a Dehn filling of a knot manifold has a left-orderablefundamental group. Our developments parallel existing results in the case ofHeegaard-Floer slope detection and foliation slope detection, leading toseveral conjectured structure theorems that connect relative Heegaard-Floerhomology and the boundary behaviour of co-oriented taut foliations with the setof left-orders supported by the fundamental group of a 3-manifold. The dynamicsof the actions of 3-manifold groups on the real line plays a key role in ourconstructions and proofs. Our analysis leads to conjectured dynamicalconstraints on such actions in the case where the underlying manifold is Floersimple.

Order-detection of slopes on the boundaries of knot manifolds