On standard forms of 1--dominations between knots with same Gromov volumes

Michel Boileau, Yi Ni, Shicheng Wang

Let $k$ and $k^{\prime }$ be two knots in 3-sphere. Say $k$ 1--dominates $k^{\prime }$, if there is a proper degree 1 map $f\co E(k)\to E(k')$, between knot exterior of $k_i$. Theorem: Suppose that…