Fixed points of automorphisms of torus knot groups

Abstract We completely classify fixed point subgroups in torus knot groups, that is, groups of the form <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>G</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy="false">⟨</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo fence="true" lspace="0em" rspace="0em">∣</m:mo> <m:mrow> <m:msup> <m:mi>x</m:mi> <m:mi>p</m:mi> </m:msup> <m: