A Golod complex with non-suspension moment-angle complex
Kouyemon Iriye, Tatsuya Yano
TL;DR
This paper presents a counterexample showing that the moment-angle complex of a Golod simplicial complex need not be homotopy equivalent to a suspension space, challenging previous assumptions.
Contribution
It introduces a specific Golod complex with a non-suspension moment-angle complex, derived from studies of Alexander duals and unions of simplicial complexes.
Findings
Counterexample to the suspension conjecture for Golod complexes
Insights into the Golod property of Alexander duals
Analysis of unions of simplicial complexes
Abstract
It could be expected that the moment-angle complex associated with a Golod simplicial complex is homotopy equivalent to a suspension space. In this paper, we provide a counter example to this expectation. We have discovered this complex through the studies of the Golod property of the Alexander dual of a join of simplicial complexes, and that of a union of simplicial complexes.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology