Ruiz Sancho, Jesús MaríaTarrés Freixenet , JuanMontesinos Amilibia, José María2023-06-202023-06-20199484-7491-510-4https://hdl.handle.net/20.500.14352/60689This 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.book parthttp://cisne.sim.ucm.es/record=b1249015~S6*spimetadata only access512.7515.17Research surveycompact smooth manifoldequivalence classvector bundleshomology classesGeometria algebraicaTopología1201.01 Geometría Algebraica1210 Topología