TL;DR
This paper develops new obstructions for Seifert fibered surgeries on knots using the mapping cone construction, impacting the understanding of knot invariants and surgery outcomes.
Contribution
It introduces novel obstructions based on the mapping cone approach, connecting Alexander polynomial, knot Floer homology, and genus invariants to Seifert fibered surgeries.
Findings
Obstructions on Alexander polynomial for Seifert fibered surgeries
Constraints on knot Floer homology related to surgery outcomes
Relations between surgery coefficient, Seifert genus, and four-ball genus
Abstract
Using the mapping cone of a rational surgery, we give several obstructions for Seifert fibered surgeries, including obstructions on the Alexander polynomial, the knot Floer homology, the surgery coefficient and the Seifert and four-ball genus of the knot.
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