Research
My interests: algebraic and combinatorial topology, in coarse geometry, Hochschild and cyclic homology theories, stable homology, representations of categories, and K-theory. I am also interested in applications of these to graph theory and neuroscience.
Accepted papers and Publications:
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Caputi, L., Cyclic homology for bornological coarse spaces. Journal of Homotopy and Related Structures (15), 2020. Available here.
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Bunke, U. and Caputi, L., Controlled objects as a symmetric monoidal functor. Higher Structures 6(1): 182-211, 2022. Available here.
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Caputi, L., Collari, C. and Di Trani, S., Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology. Journal of Algebraic Combinatorics 57: 617–658 (2023). Available here.
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Caputi, L., Celoria, D. and Collari, C. Categorifying connected domination via graph überhomology. Journal of Pure and Applied Algebra 227(9), 2023. Available online here, or at arXiv:2201.00721 .
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Caputi, L. and Riihimäki, H. Hochschild homology, and a persistent approach via connectivity digraphs, 2023. Journal of Applied and Computational Topology. Available online here and at the link arXiv:2204.00462 .
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Caputi, L., Celoria, D. and Collari, C. From the Mayer-Vietoris spectral sequence to überhomology, 2023. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 1-24. doi:10.1017/prm.2023.104 Available also at the arXiv:2304.10134 .
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Caputi, L., Collari, C., Di Trani, S., and Smith, J. P. , On the Homotopy Type of Multipath Complexes, 2024. Mathematika, 70: e12235, https://doi.org/10.1112/mtk.12235. Available online at ArXiv:2208.04656 .
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Caputi, L., Celoria, D. and Collari, C. Monotone cohomologies and oriented matchings, 2022. Accepted for publication on Homology, Homotopy and Applications. Available online at the arXiv:2203.03476v1 .
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Caputi, L., Collari, C. and Di Trani, S., Multipath cohomology of directed graphs. Accepted for publication on Algebraic & Geometric Topology. Available online at the arXiv:2108.02690 .
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Caputi, L. and Riihimäki, H. On reachability categories and commuting algebras of quivers, 2023. Accepted for publication on Theory and Applications of Categories. Available online at the arXiv:2306.15388 .
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Bunke, U. and Caputi, L., Localization for coarse homology theories, 2019. Accepted for publication on Annals of K-theory. Available at the arXiv:1902.04947 .
Publications in applied mathematics:
- Caputi, L., Pidnebesna, A. and Hlinka, J., Promises and pitfalls of Topological Data Analysis for brain connectivity analysis. Neuroimage 2021, vol. 238. Available here. Companion software available here.
Preprints:
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Caputi, L., and Collari, C., On finite generation in magnitude (co)homology, and its torsion, 2023. Available online at the arXiv:2302.06525 .
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Caputi, L., Collari, C., and Ramos, E. The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology, 2024. Available online at the arXiv:2401.01248 .
PhD Thesis:
Hochschild and cyclic homology for bornological coarse spaces, PhD thesis, University of Regensburg, 2019. Available here.
Recent recorded seminars:
01/11/2023, From the Mayer-Vietoris spectral sequence to überhomology available on Youtube, Cohomology in algebra, geometry, physics and statistics seminars, Institute of Mathematics of the Czech Academy of Sciences, Prague
10/04/2024, The weak categorical quiver minor theorem and its applications available here, BIMSA Topology Seminar, online