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The Topological Interpretation of the Core Group of a Surface in S4

Published online by Cambridge University Press:  20 November 2018

Józef H. Przytycki  and
Witold Rosicki
Józef H. Przytycki
Affiliation:
Department of Mathematics, George Washington University and University of Maryland, College Park, email: przytyck@gwu.edu
Witold Rosicki
Affiliation:
Institute of Mathematics, Gdańsk University, email: wrosicki@math.univ.gda.pl
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Abstract

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We give a topological interpretation of the core group invariant of a surface embedded in ${{S}^{4}}\,\left[ \text{F-R} \right],\,\left[ \text{Ro} \right]$. 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.

Keywords

57Q4557M1257M05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 131 - 137
Copyright
Copyright © Canadian Mathematical Society 2002

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