Satellite Manifolds

Oziride Manzoli Neto
Institute of Mathematical Science, University of São Paulo
E-mail: ozimneto@icmc.sc.usp.br

$\line (1,0){344}$

Let $V_{F} {\cong}_{\phi} F^{k}\times D^{2}$ be a tubular neighborhood of an embedding of an orientable manifold F^k in S^k+2. In this work we define embeddings of certain manifolds M^k in V_F. 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 F^k. We call these manifolds satellites of F^k, 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 S^k+2-V_M. 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