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The course teaches how to use star clusters in clique complexes and the Vietoris-Rips complex of planar sets to obtain homotopy information. The learning outcomes include understanding the concept of star clusters, their applications in homotopy invariants of independence complexes of graphs, and obtaining homotopy information of the Vietoris-Rips complex. The course covers topics such as independence complexes of graphs, proofs, applications, and other homotopic types. The teaching method involves theoretical explanations and collaborative results. The intended audience for this course includes individuals interested in algebraic topology, homotopy theory, and simplicial complexes.
