Problemas de algebricidad en topología diferencial

Abstract

This is a research survey on results dealing with the following question: Let M be a compact smooth manifold and A a family of geometric objects related to M such that there exists some natural equivalence of the pairs (M,A). Does every equivalence class contain some kind of algebraic representative? The survey deals with the cases A = ∅, presenting the achievements of the work of Seifert-Nash-Tognoli, with vector bundles and with realizations of homology classes. In cases of particular interest the methods of proof are outlined.