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 pants graph has proved to be influential in understanding 3-manifoldsconcretely. This stems from a quasi-isometry between the pants graph and theTeichm\"uller space with the Weil-Petersson metric. Currently, all estimates onthe quasi-isometry constants are dependent on the surface in an undiscoveredway. This paper starts effectivising some constants which begins theunderstanding how relevant constants change based on the surface. We do this bystudying the hyperbolicity constant of the pants graph for the five-puncturedsphere and the twice punctured torus. The hyperbolicity constant of therelative pants graph for complexity 3 surfaces is also calculated. Note, forhigher complexity surfaces, the pants graph is not hyperbolic or even stronglyrelatively hyperbolic.

Hyperbolicity constants for pants and relative pants graphs