Floer lasagna modules for some 2-handlebodies

@misc{alishahi2026floer,
  title = {{Floer lasagna modules for some 2-handlebodies}},
  author = {Akram Alishahi and Eugene Gorsky and Beibei Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34744},
  eprint = {2610.34744},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34744},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - Floer lasagna modules for some 2-handlebodies
AU  - Akram Alishahi
AU  - Eugene Gorsky
AU  - Beibei Liu
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34744
UR  - https://arxiv.org/abs/2610.34744
AB  - Morrison, Walker and Wedrich used Khovanov homology to define the skein lasagna module for a 4-manifold with a link in its boundary. The skein lasagna module was shown to be a deep and powerful invariant; in particular, Ren and Willis proved that it detects exotic smooth structures. Still, computing the skein lasagna module outside some carefully chosen grading range remains an important open problem. Motivated by this construction, Chen defined the Floer lasagna module using Heegaard Floer link homology. In this paper, we give a complete, but partially conjectural description of Floer lasagna modules for a class of 4-manifolds obtained by adding 2-handles along plumbed L-space knots (with certain framing constraints). In particular, we prove that for ℂℙ^2̅ it is infinite-dimensional, and conjecture that for ℂℙ^2 it is infinite-dimensional as well. We compute this module for ℂℙ^2̅ (and conjecturally for ℂℙ^2) in all Alexander and Maslov gradings. This strengthens and extends the recent results of McCulloch.
ER  -