preprint submitted Yossi Bleile author 920a7385-7995-11ef-9bfd-8c434cd8f3c20000-0002-4861-9174 Lisbeth Fajstrup author Teresa Heiss author 4879BB4E-F248-11E8-B48F-1D18A9856A870000-0002-1780-2689 Anne Marie Svane author Søren Strandskov Sørensen author HeEd department Alpha Shape Theory Extended project Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times. 2025 eng 2505.1785810.48550/arXiv.2505.17858 Bokor Bleile, Yossi, et al. “Identifying Cobordisms Using Kernel Persistence.” <i>ArXiv</i>, 2505.17858, doi:<a href="https://doi.org/10.48550/arXiv.2505.17858">10.48550/arXiv.2505.17858</a>. Y. Bokor Bleile, L. Fajstrup, T. Heiss, A. M. Svane, and S. S. Sørensen, “Identifying cobordisms using kernel persistence,” <i>arXiv</i>. . Bokor Bleile, Yossi, Lisbeth Fajstrup, Teresa Heiss, Anne Marie Svane, and Søren Strandskov Sørensen. “Identifying Cobordisms Using Kernel Persistence.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2505.17858">https://doi.org/10.48550/arXiv.2505.17858</a>. Bokor Bleile, Y., Fajstrup, L., Heiss, T., Svane, A. M., &#38; Sørensen, S. S. (n.d.). Identifying cobordisms using kernel persistence. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2505.17858">https://doi.org/10.48550/arXiv.2505.17858</a> Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2505.17858">10.48550/arXiv.2505.17858</a> Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv (n.d.). Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. arXiv, 2505.17858. 210162026-01-20T10:12:21Z2026-07-22T06:33:07Z