On the nonvanishing of Floer lasagna modules

@misc{zhu2026nonvanishing,
  title = {{On the nonvanishing of Floer lasagna modules}},
  author = {Kai Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00830},
  eprint = {2611.00830},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00830},
}

TY  - UNPB
TI  - On the nonvanishing of Floer lasagna modules
AU  - Kai Zhu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00830
UR  - https://arxiv.org/abs/2611.00830
AB  - In this paper, we establish several nonvanishing results for Floer lasagna modules ℱℒ(W,K) for a smooth compact connected oriented $4$-manifold W and a knot K⊂ ∂ W, via the evaluation maps to link Floer homology. We first establish a general criterion: if a certain Heegaard Floer cobordism map associated with a smooth $4$-manifold W is nonzero, then ℱℒ(W,U)≠ 0, where U⊂ ∂ W is a local unknot. Applications include the nonvanishing of Floer lasagna modules for #^mℂP^2̅ and for knot traces X_n(K) when K is slice and n is a non-positive integer. In another direction, we show that for every nontrivial knot K and every integer n, the Floer lasagna module ℱℒ(X_n(K),K_n) is nonzero, where K_n⊂ S_n^3(K) is the dual knot. Moreover, if K is an L-space knot, then ℱℒ(X_n(K),K_n) is infinite-dimensional for all integers n≥ max{2g(K),1}.
ER  -