
TL;DR
This paper introduces the concept of L-space links, explores their properties and examples, and provides methods to compute their Floer homology and classify L-space surgeries, expanding understanding of hyperbolic 3-manifolds.
Contribution
It initiates a comprehensive study of L-space links, including their properties, examples, and computational techniques for Floer homology and surgery classification.
Findings
Many hyperbolic L-space links identified, including chain and two-bridge links.
Bounds established on link Floer homology ranks and Alexander polynomial coefficients.
Provided algorithms for classifying L-space surgeries and computing Floer homology.
Abstract
An -space link is a link in on which all large surgeries are -spaces. In this paper, we initiate a general study of the definitions, properties, and examples of -space links. In particular, we find many hyperbolic -space links, including some chain links and two-bridge links; from them, we obtain many hyperbolic -spaces by integral surgeries, including the Weeks manifold. We give bounds on the ranks of the link Floer homology of -space links and on the coefficients in the multi-variable Alexander polynomials. We also describe the Floer homology of surgeries on any -space link using the link surgery formula of Ozsv\'{a}th and Manolescu. As applications, we compute the graded Heegaard Floer homology of surgeries on 2-component -space links in terms of only the Alexander polynomial and the surgery framing, and give a fast algorithm to classify -space…
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