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Satellite Manifolds

Oziride Manzoli Neto
Institute of Mathematical Science, University of São Paulo

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Let $V_{F} {\cong}_{\phi} F^{k}\times D^{2}$ be a tubular neighborhood of an embedding of an orientable manifold Fk in Sk+2. In this work we define embeddings of certain manifolds Mk in VF. These manifolds are defined in such a way that the map $\pi :V{\cong}_{\phi} F^{k}\times D^{2} \rightarrow F^{k}$ restricted to M is an n-covering map of Fk. We call these manifolds satellites of Fk, since it is a generalization of a satellite construction in the classical case. We study the relation between the Alexander Modules of the two embeddings using a special decomposition of the Abelian Covering $\tilde X_{M}$ of Sk+2-VM. For the case of orientable surfaces in S4 we are able to get better relations and examples.

Keywords: Alexander Modules; Knot Theory; Satellite Manifolds.
AMS classification: 57M25


Tohru Okuzono