Eduardo Santillan - Topological properties of removable singularities for analytic functions

A closed set X of a complex manifold M is said to be a removable singularity if every analytic function defined on M-Xhas got an analytic extension to M. In his doctoral tesis, Shiffman proved a partial characterisation of the removable singularities by using the Hausdorff measure. Moreover, in 1994, professors Chirca, Stout and Lupacciolu showed more results which are completely independet of those of Shiffman; they used the cover dimension. The actual challenge is to improve that results to characterise the removable singularities by using just topological properties.