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Fixed-point-free
pseudo-Anosov homeomorphisms, knot Floer homology and the
cinquefoil
Ethan Farber, Braeden Reinoso and Luya Wang |
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Geometry & Topology 28 (2024) 4337–4381
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Abstract |
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Given any genus-two, hyperbolic, fibered knot in with nonzero fractional Dehn twist coefficient, we show that its pseudo-Anosov representative has a fixed point. Combined with recent work of Baldwin, Hu and Sivek, this proves that knot Floer homology detects the cinquefoil knot , and that the cinquefoil is the only genus-two L-space knot in . Our results have applications to Floer homology of cyclic branched covers over knots in , to –abelian Dehn surgeries, and to Khovanov and annular Khovanov homology. Along the way to proving our fixed point result, we describe a small list of train tracks carrying all pseudo-Anosov homeomorphisms in most strata on the punctured disk. As a consequence, we find a canonical track carrying all pseudo-Anosov homeomorphisms in a particular stratum on the genus-two surface, and describe every fixed-point-free pseudo-Anosov homeomorphism in . |
Keywords
pseudo-Anosov homeomorphism, knot Floer homology, train
track, fibered knot, fixed point
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Mathematical Subject Classification
Primary: 37E30, 57K18
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References |
Publication
Received: 1 February 2023
Revised: 10 April 2023
Accepted: 12 May 2023
Published: 27 December 2024
Proposed: Ciprian Manolescu
Seconded: Mladen Bestvina, David Gabai
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Authors |
| Ethan Farber | |
| Boston College Chestnut Hill, MA United States |
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| Braeden Reinoso | |
| Boston College Chestnut Hill, MA United States |
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| Luya Wang | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
Institute for Advanced Study Princeton, NJ United States |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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