Knot groups in S 4 with nontrivial homology
1982; Mathematical Sciences Publishers; Volume: 103; Issue: 2 Linguagem: Inglês
10.2140/pjm.1982.103.315
ISSN1945-5844
AutoresAndrew M. Brunner, E. J. Mayland, Jonathan Simon,
Tópico(s)Geometric and Algebraic Topology
ResumoIn this paper we exhibit smooth 2-manifolds F 2 in the 4-sphere S 4 having the property that the second homology of the group π 1 (S i -F 2 ) is nontrivial.In particular, we obtain tori for which H 2 {π x )=Z 2 and, by forming connected sums, surfaces of genus n for which i^fe) is the direct sum of n copies of Z 2 .Corollaries include: (1) There are knotted surfaces in S 4 that cannot be constructed by forming connected sums of unknotted surfaces and knotted 2-spheres.(2) The class of groups that occur as knot groups of surfaces in S 4 is not contained in the class of high dimensional knot groups of S n in S n+2 .
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