Knot Floer homology and fixed points

Yi Ni

Knot Floer homology and fixed points

Geometric Topology 2026-05-07 v2 Symplectic Geometry

Authors: Yi Ni

Abstract

If $K$ is a fibered knot in a closed, oriented $3$ --manifold $Y$ with fiber $F$ , and $\widehat{HFK}(Y,K,[F], g(F)-1;\mathbb Z/2\mathbb Z)$ has rank $r$ , then the monodromy of $K$ is freely isotopic to a diffeomorphism with at most $r-1$ fixed points. This generalizes earlier work of Baldwin--Hu--Sivek and Ni. We also clarify a misleading formula in Cotton-Clay's computation of the symplectic Floer homology of mapping classes of surfaces.

Keywords

floer homology knot theory algebraic topology

Cite

@article{arxiv.2201.10546,
  title  = {Knot Floer homology and fixed points},
  author = {Yi Ni},
  journal= {arXiv preprint arXiv:2201.10546},
  year   = {2026}
}

Comments

13 pages. V2: We incorporate the referee's comments, and restructured Section 4 to include an overlooked case (Proposition 4.4). This is the version accepted for publication by the Journal of Topology

Knot Floer homology and fixed points

Abstract

Keywords

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