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

We provide a new obstruction for a rational homology 3‐sphere to arise by Dehn surgery on a given knot in the 3‐sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient and a count of  L ‐ structures  on the 3‐manifold, that is spin  c  ‐structures with the simplest possible associated Heegaard Floer group. Applications include an obstruction for two framed knots to yield the same 3‐manifold, an obstruction that is particularly effective when working with families of framed knots. We introduce the  rational and integral Dehn surgery genera  for a rational homology 3‐sphere, and use our inequality to provide bounds, and in some cases exact values, for these genera. We also demonstrate that the difference between the integral and rational Dehn surgery genera can be arbitrarily large.

Heegaard Floer genus bounds for Dehn surgeries on knots