1 results
Thin links and Conway spheres
- Part of
-
- Journal:
- Compositio Mathematica / Volume 160 / Issue 7 / July 2024
- Published online by Cambridge University Press:
- 20 May 2024, pp. 1467-1524
- Print publication:
- July 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal
$\delta$-grading. This leads to the broader class of thin links that one would like to characterize without reference to the invariant in question. We provide a relative version of thinness for tangles and use this to characterize thinness via tangle decompositions along Conway spheres. These results bear a strong resemblance to the L-space gluing theorem for three-manifolds with torus boundary. Our results are based on certain immersed curve invariants for Conway tangles, namely the Heegaard Floer invariant 
$\operatorname {HFT}$ and the Khovanov invariant 
$\widetilde {\operatorname {Kh}}$ that were developed by the authors in previous works.
