Independence complexes of circle graphs

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

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arXiv · 2412.01125

Independence complexes of circle graphs

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

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Abstract

Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link $L$, they reveal topological properties of $L$, more specifically, of its Khovanov homology. We analyze the homotopy type of independence complexes of circle graphs, with a focus on those arising when the graph is bipartite. Moreover, we compute (real) extreme Khovanov homology of a $4$-strand pretzel knot using chord diagrams and independence complexes.

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BibTeX RIS

Rhea Palak Bakshi, Ali Guo, Dionne Ibarra, Gabriel Montoya-Vega, Sujoy Mukherjee, Marithania Silvero, Jonathan Spreer. 2024-12-02. Independence complexes of circle graphs. https://arxiv.org/abs/2412.01125

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