标题： 曲面在S^4中的核心群的拓扑解释 显示英文标题

标题： The topological interpretation of the core group of a surface in S^4

摘要： 我们给出了嵌入在S^4中的曲面的核心群不变量的拓扑解释。 我们证明该群同构于以曲面为分支集的S^4的二重分支覆盖的基本群与无限循环群的自由积。 我们提出了对非定向曲面、其他循环分支覆盖以及其他在球面上的流形的余维二嵌入的一般化。 计算n次循环分支覆盖的基本群的方法与R.H.Crowell在《置换表示的导出群》（Adv. in Math. 53(1), 1984, 99--124）中描述的方法有关。 我们在最近的论文中使用了这些计算：http://front.math.ucdavis.edu/math.GT/0302098 http://front.math.ucdavis.edu/math.GT/0309140 显示英文摘要

摘要： We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S^4 with the surface as a branched set, and the infinite cyclic group. We present a generalization for unoriented surfaces, for other cyclic branched covers, and other codimension two embeddings of manifolds in spheres. The method of computing the fundamental group of n-fold cyclic branched covers is related to the one described in R.H.Crowell, The derived group of a permutation representation, Adv. in Math. 53(1), 1984, 99--124. We use these computations in recent papers: http://front.math.ucdavis.edu/math.GT/0302098 http://front.math.ucdavis.edu/math.GT/0309140