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The Topological Interpretation of the Core Group of a Surface in $S^4$

  Published:2002-03-01
 Printed: Mar 2002
  • Józef H. Przytycki
  • Witold Rosicki
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Abstract

We give a topological interpretation of the core group invariant of a surface embedded in $S^4$ \cite{F-R}, \cite{Ro}. 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.
MSC Classifications: 57Q45, 57M12, 57M05 show english descriptions Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Special coverings, e.g. branched
Fundamental group, presentations, free differential calculus
57Q45 - Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
57M12 - Special coverings, e.g. branched
57M05 - Fundamental group, presentations, free differential calculus
 

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