Helly's theorem for systolic complexes

2014/05/20 by Krzysztof Święcicki, Święcicki, Krzysztof
Computer Science · Mathematics · #20F65 (Primary) 14F05 #52A35 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1405.5194

openalex publication_date 2014/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the analogue of Helly's theorem for systolic complexes. Namely, we show that 7-systolic complexes have Helly dimension less or equal to 1, whereas 6-systolic complexes have Helly dimension bounded from the above by 2.

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