Topological simplification guided by forbidden regions LIPIcs Leśkiewicz, Jakub Furmanek, Bartosz Lipiński, Michał ; https://orcid.org/0000-0001-9789-9750 Morozov, Dmitriy persistent homology topological simplification depth posets ddc:500 Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c⋅n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex. Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2026 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/22002 https://research-explorer.ista.ac.at/download/22002/22110 Leśkiewicz J, Furmanek B, Lipiński M, Morozov D. Topological simplification guided by forbidden regions. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.72">10.4230/LIPIcs.SoCG.2026.72</a> eng info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPIcs.SoCG.2026.72 info:eu-repo/semantics/altIdentifier/e-issn/1868-8969 info:eu-repo/semantics/altIdentifier/isbn/9783959774185 info:eu-repo/semantics/altIdentifier/arxiv/2603.16416 info:eu-repo/semantics/openAccess