Equivariant bordism classification of five-dimensional (ℤ₂)³-manifolds with isolated fixed points

2025/04/14 by Y. H. Guan, Zhi Lü, Guan, Yuanxin +1 · 1 citation
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2504.09988

openalex publication_date 2025/04/14 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Denote by Z₅((ℤ₂)³) the group, which is also a vector space over ℤ₂, generated by equivariant unoriented bordism classes of all five-dimensional closed smooth manifolds with effective smooth (ℤ₂)³-actions fixing isolated points. We show that dim_ℤ2 Z₅((ℤ₂)³) = 77 and determine a basis of Z₅((ℤ₂)³), each of which is explicitly chosen as the projectivization of a real vector bundle. Thus this gives a complete classification up to equivariant unoriented bordism of all five-dimensional closed smooth manifolds with effective smooth (ℤ₂)³-actions with isolated fixed points.

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