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

http://dx.doi.org/10.4153/CMB-2002-016-0
Canad. Math. Bull. 45(2002), 131-137

  Published:2002-03-01
 Printed: Mar 2002

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.