منابع مشابه
KNOTTED CONTRACTIBLE 4-MANIFOLDS IN S4 W.B.R. Lickorish
A construction will here be described that can produce a compact contractible 4-manifold M embedded piecewise linearly (or smoothly) in S4 with the fundamental group of its complement being nontrivial. Then, another embedding of M in S4 will be produced which has simply connected complement. Several examples of this will be given. Of course, the construction emphasizes that contractible spaces ...
متن کاملKnotted Surfaces in 4-manifolds
Fintushel and Stern have proved that if Σ ⊂ X is a symplectic surface in a symplectic 4-manifold such that Σ has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent but smoothly distinct embedded surfaces homologous to Σ. Here we extend this result to include symplectic surfaces whose self-intersection is bounded below by 2− 2g,...
متن کاملObservations on Lickorish Knotting of Contractible 4–manifolds
Lickorish has constructed large families of contractible 4–manifolds that have knotted embeddings in the 4–sphere and has also shown that every finitely presented perfect group with balanced presentation occurs as the fundamental group of the complement of a knotted contractible manifold. Here we make a few observations regarding Lickorish’s construction, showing how to extend it to construct c...
متن کاملTopological Triviality of Smoothly Knotted Surfaces in 4-manifolds
Some generalizations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are standard, then these surfaces are topologically unknotted.
متن کاملKNOTTED CONTRACIBLE 4-MANIFOLDS IN THE 4-SPHERE by W.B.Raymond Lickorish
Examples are given to show that some compact contractible 4-manifolds can be knotted in the 4-sphere. It is then proved that any finitely presented perfect group is a knot group for an embedding of some contractible 4-manifold in S.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2003
ISSN: 0030-8730
DOI: 10.2140/pjm.2003.208.283