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arXiv · 2609.38117

Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers

Jinzhou Huang
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Abstract

In [OS05] the authors proved an exact triangle for the Heegaard Floer homology of the double branched covers associated to a skein sequence of links, and constructed a spectral sequence from the reduced Khovanov homology to the Heegaard Floer homology of the double branched cover of a link. For $L \subset S^3$ a link and $Σ(L)$ its double branched cover, the invariant $HF(Σ(L))$ doesn't capture the information of the natural involution on $Σ(L)$. In this paper we study the equivariant version of $HF(Σ(L))$ and prove that similar exact triangle and spectral sequence hold for this equivariant version.

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Jinzhou Huang. 2026-09-29. Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers. https://arxiv.org/abs/2609.38117

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