论文标题
拓扑结集团上的等级卫星操作员
Rank-expanding satellite operators on the topological knot concordance group
论文作者
论文摘要
给定固定的打结p在固体圆环中，并在s^3中的任何结k，都可以与图案的卫星形成k的卫星。此操作会诱导s^3中的一致性结组的自图。 Dai，Hedden，Mallick和Stoffregen证明了在平滑类别中存在此功能范围扩展的P；也就是说，对于某些k，集合{p（nk）}生成一个无限的等级子组。在这里，我们证明了在拓扑局部平坦的一致性组中也存在类似的例子。这些例子在代数一致组中不存在。
Given a fixed knot P in a solid torus and any knot K in S^3, one can form the satellite of K with pattern P. This operation induces a self-map of the concordance group of knots in S^3. It has been proved by Dai, Hedden, Mallick, and Stoffregen that in the smooth category there exist P for which this function is rank-expanding; that is, for some K, the set {P(nK)} generates an infinite rank subgroup. Here we demonstrate that similar examples exist in the case of the topological locally flat concordance group. Such examples cannot exist in the algebraic concordance group.
