2011/11/29 by Jun‐Da Chen, Junda Chen, Chen, Junda +4 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT
paper · pdf · doi:10.48550/arxiv.1111.6699
34 pages with 6 figures; v2 revised and corrected
openalex publication_date 2011/11/29 · arxiv created 2012/11/05 · arxiv updated 2012/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology, such as small covers, quasi-toric manifolds and (real) moment-angle manifolds; especially for the cases of small covers and quasi-toric manifolds. These kinds of orbit configuration spaces are all non-free and noncompact, but still built via simple convex polytopes. We obtain an explicit formula of Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope. As a by-product of our method, we also obtain a formula of Euler characteristic for the classical configuration space, which generalizes the Félix-Thomas formula. In addition, we also study the homotopy type of such orbit configuration spaces. In particular, we determine an equivariant strong deformation retract of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold, which turns out that we are able to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence.