2007/05/27 by Alessandro Berarducci, ALESSANDRO BERARDUCCI, Antongiulio Fornasiero +1 · 6 citations
Computer Science · Mathematics · #Advanced Topology and Set Theory #Betti number #Closure (psychology) #Cohomology #Finitely-generated abelian group #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Locally compact group #Locally compact space #Set (abstract data type) #Topological and Geometric Data Analysis #math.AT #math.LO #msc:03C64 #msc:14P25 #msc:55N30
paper · pdf · doi:10.1142/s0219061309000859
published in Journal of Mathematical Logic 09(02), 167-182 (World Scientific) · 28 pages, 7 figures and diagrams Added the hypothesis that singletons are construcible to section 3. Corrected misprints
arxiv created 2007/05/27 · openalex publication_date 2009/12/01 · arxiv updated 2010/09/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language.