algebraic topology

On small covers over Bier spheres

arXiv:2607.28141

summary

The paper classifies real toric manifolds (small covers) over Bier spheres that arise from the skeleta of a simplex, determines their homeomorphism types for certain skeleta, and computes rational Betti numbers for the remaining cases.

Abstract

The Bier sphere of a simplicial complex is defined as the deleted join of and its combinatorial Alexander dual. We focus on the class of Bier spheres of the skeleta of a simplex. Since these Bier spheres are known to be polytopal, they give rise to small covers. We classify small covers over these Bier spheres up to Davis--Januszkiewicz equivalence. As applications, for all , we determine the homeomorphism types of small covers over the Bier spheres of the -skeleton and the -skeleton of an -simplex. For the remaining cases , we compute their rational Betti numbers.

15 pages with 1 figure and 1 table

Topics & keywords

#small covers#bier spheres#simplicial complexes#polytopal spheres#davis‑januszkiewicz equivalence#betti numbersBier spheresmall coverDavis‑Januszkiewicz equivalencerational Betti numbersskeleta of simplexcombinatorial Alexander dual
On small covers over Bier spheres · wovepaper