Toric wedge induction and toric lifting property for piecewise linear spheres with a few vertices

2024/04/24 by Suyoung Choi, Hyeontae Jang, Choi, Suyoung +3
Engineering · Mathematics · #57S12 #Advanced Materials and Mechanics #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2404.15600

openalex publication_date 2024/04/24 · openalex created_date 2024/04/26 · openalex updated_date 2026/07/28

Abstract

Let K be an (n-1)-dimensional piecewise linear sphere on [m], where m≤ n+4. There are a canonical action of m-dimensional torus T^m on the moment-angle complex Z_K, and a canonical action of ℤ₂^m on the real moment-angle complex ℝZ_K, where ℤ₂ is the additive group with two elements. We prove that any subgroup of ℤ₂^m acting freely on ℝZ_K is induced by a subtorus of T^m acting freely on Z_K. The proof primarily utilizes a suitably modified method of toric wedge induction and the combinatorial structure of a specific binary matroid of rank 4.

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