O-minimal cohomology and definably compact definable groups

2000/12/07 by Mario J. Edmundo, Mário J. Edmundo, Edmundo, Mario J. · 2 citations
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, Reasoning, and Knowledge #math.AT #math.LO

paper · pdf · doi:10.48550/arxiv.math/0012050

71 pages, (December 16, 2000-submitted)

openalex publication_date 2000/12/07 · arxiv created 2001/01/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let N be an o-minimal expansion of a real closed field. We develop cohomology theory for the category of N-definable manifolds and N-definable maps, and use this to solve the Peterzil-Steinhorn problem on the existence of torsion points on N-definably compact N-definable abelian groups. We compute the cohomology rings of N-definably compact N-definable groups, and we prove an o-minimal analog of the Poincare duality theorem, the Alexander dualti theorem, the Lefschetz duality theorem and the Lefschetz fixed point theorem.

Cited by

• On the de Rham theorem in the globally subanalytic setting
• On Definably Compact Semigroups in o-Minimal Structures

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