The wedge-of-spheres conjecture for independence complexes of bipartite circle graphs
The wedge-of-spheres conjecture for independence complexes of bipartite circle graphs
Let be a bipartite circle graph, namely a circle graph that is bipartite, and let be its independence complex, whose simplices are the subsets of pairwise non-adjacent vertices of . Bipartite wedge-of-spheres conjecture. The independence complex associated to a bipartite circle graph is homotopy equivalent to a wedge of spheres. This is the restriction relevant to Lando graphs, since the family of Lando graphs coincides with the family of bipartite circle graphs. If true, the conjecture would imply that the extreme Khovanov homology of any diagram is torsion-free and provide an obstruction to a link being Khovanov -adequate. Its status is not resolved in the supplied source.
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Primary source
Lizzie Buchanan, Huizheng Guo, Gabriel Montoya-Vega, Yongwu Rong and Marithania Silvero, “On the notion of Khovanov A-adequacy”, arXiv:2502.17637 (2025).
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