Suppose that there exists an epimorphism from the knot group of a 2–bridge knot onto that of another knot . We study the relationship between their crossing numbers and . More specifically, it is shown that is greater than or equal to , and we estimate how many knot groups a 2–bridge knot group maps onto. Moreover, we formulate the generating function which determines the number of 2–bridge knot groups admitting epimorphisms onto the knot group of a given 2–bridge knot.
"Epimorphisms between $2$–bridge knot groups and their crossing numbers." Algebr. Geom. Topol. 17 (4) 2413 - 2428, 2017. https://doi.org/10.2140/agt.2017.17.2413