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

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

2004-03-26

arxiv.org/abs/math/0403475v1

Canad. Math. Bull., 45(1), 2002, pp. 131-137

Mathematics

Geometric Topology

9 pages, 1 figure

Scientific paper

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

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