2019/11/29 by Wolfgang Pitsch, Jérôme Scherer
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Cohomology #Combinatorics #Computer science #Euclidean geometry #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Space (punctuation) #Topology (electrical circuits) #math.AT
paper · pdf · doi:10.1017/prm.2020.24
published as Proceedings of the Royal Society of Edinburgh: Section A Mathematics 151 (2021) 509-524 · 16 pages
arxiv created 2019/11/29 · openalex publication_date 2020/04/08 · arxiv updated 2021/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classical examples of complex projective spaces under complex conjugation. Spaces which are constructed from unit balls in complex Euclidean spaces are called spherical and are very well understood. Our aim is twofold. We construct ‘exotic’ conjugation spaces and study the realization question: which spaces can be realized as real loci, i.e., fixed points of conjugation spaces. We identify obstructions and provide examples of spaces and manifolds which cannot be realized as such.