ALEXANDER MODULES OF ORIENTABLE SURFACES IN 4-SPHERE

Rui Marcos de Oliveira BARROS[1]

Oziride MANZOLI NETO[2]

§    ABSTRACT: For an embedding (differentiable or piecewise linear locally flat) of an orientable surface in the four sphere S4, one can construct, similarly to the case of knots an links, a canonical ciclic covering of the complement X of the surface in S4 . The homology groups of are modules over L = [t,t -1] and they are source of many invariants of the class of the embedding. In this work we present some of these properties ( including classification and realization theorems ).

§    KEYWORDS: Alexander Modules; Knot Theory.

 



[1] Departamneto de Matemática - FC - UNESP - 17033 - Bauru - SP - Brasil.

[2] Departamento de Matemática - Instituto de Ciências Matemáticas de São Carlos - USP - 13560-970 - São Carlos - SP - Brasil.