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Independence complexes of circle graphs are purely combinatorial objects. However, when derived from a diagram of a link L, they encode rich topological information – particularly about the Khovanov homology of L. In this work, we investigate the homotopy types of independence complexes of circle graphs, with a focus on the case where the graph is bipartite. Moreover, we compute the extreme Khovanov homology of the family of pretzel links P(q, r, s,−t) with q, r, s, t > 0, using chord diagrams and their corresponding independence complexes.

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Independence complexes of circle graphs

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  • 发表日期：

    2026年

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  • Rhea Palak Bakshi,
  • Ali Guo,
  • Dionne Ibarra,
  • Gabriel Montoya-Vega,
  • Sujoy Mukherjee,
  • Marithania Silvero,
  • Jonathan Spreer

摘要

Independence complexes of circle graphs are purely combinatorial objects. However, when derived from a diagram of a link L, they encode rich topological information – particularly about the Khovanov homology of L. In this work, we investigate the homotopy types of independence complexes of circle graphs, with a focus on the case where the graph is bipartite. Moreover, we compute the extreme Khovanov homology of the family of pretzel links P(q, r, s,−t) with q, r, s, t > 0, using chord diagrams and their corresponding independence complexes.