Fixed-point-free pseudo-Anosov homeomorphisms, knot Floer homology and the cinquefoil

Ethan Farber, Braeden Reinoso, Luya Wang

Given any genus-two, hyperbolic, fibered knot in $S^3$ with nonzero fractional Dehn twist coefficient, we show that its pseudo-Anosov representative has a fixed point. Combined wit…