AI 中文总结
针对具有特定抛物不动点的有理映射对，构造双次数\((pq,pq)\)的代数对应\(F\)实现映射复合与循环群自由积表示的交配，表明\(F\)是特定有理映射删除覆盖对应之复合，推广方法构造多项式对复合与群表示的交配，给出不可逆例子。
AI 中文摘要
给定一对次数为\(p\)和\(q\)的有理映射\((f,g)\)，它们各自具有一个抛物不动点且有一个完全不变的单连通吸引盆。我们在黎曼球面上构造了一个双次数为\((pq,pq)\)的代数对应\(F\)，实现了映射的两个复合\(g\circ f\)和\(f\circ g\)与阶为\(p + 1\)和\(q + 1\)的循环群的自由积的抛物忠实离散表示之间的交配。我们还表明\(F\)是一对与次数为\(p + 1\)和\(q + 1\)的多项式共轭的有理映射的删除覆盖对应的复合。我们将方法推广到构造多项式对的复合与同一群的（非抛物）忠实克莱因表示之间的交配，现在正则集是连通的。据我们所知，这些映射对和群之间的交配是首批不可逆的例子（即它们不与自身的逆共轭）。
英文摘要
Given a pair of rational maps $(f, g)$, of degrees $p$ and $q$, each with a parabolic fixed point having a fully invariant simply-connected basin of attraction, we construct an algebraic correspondence $F$ on the Riemann sphere, of bidegree $(pq, pq)$, realizing a mating between the two compositions $g\circ f$ and $f\circ g$ of the maps, and the parabolic faithful discrete representation of the free product of cyclic groups of orders $p + 1$ and $q + 1$. We also show that $F$ is the composition of a pair of deleted covering correspondences of rational maps which are conjugated to polynomials of degrees $p + 1$ and $q + 1$. We generalize our method to construct matings between compositions of pairs of polynomials and (non-parabolic) faithful Kleinian representations of the same group, now with connected regular set. As far as we are aware, these matings between pairs of maps and groups are the first examples that are not time-reversible (that is, they are not conjugate to their own inverses).
Comments27 pages, 13 figures
