Nearly fibered links with genus one

DOI10.1007/S10474-023-01364-0arXiv2302.12365MaRDI QIDQ6057449

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Publication date: 4 October 2023

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Abstract: We classify all the $n$-component links in the $3$-sphere that bound a Thurston norm minimizing Seifert surface $Sigma$ with Euler characteristic $chi(Sigma)=n-2$ and that are nearly fibered, which means that their rank of the maximal (collapsed) Alexander grading $s_{exttop}$ of the link Floer homology group $widehatHFL$ is equal to two. In other words, such a link $L$ satisfies $s_{exttop}=fracn-chi(Sigma)2=1$, and in addition $extrk:widehat{HFL}_{\ast }(L)[1]=2$ and $extrk:widehat{HFL}_{\ast }(L)[s]=0$ for every $s>1$. The proof of the main theorem is inspired by the one of a similar recent result for knots by Baldwin and Sivek; and involves techniques from sutured Floer homology. Furthermore, we also compute the group $widehatHFL$ for each of these links.

Full work available at URL: https://arxiv.org/abs/2302.12365

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