Applications of Algebraic Topology
Rational Homotopy Theory
Lusternik-Schnirelmann category
C. Faustino, T. Kahl, The homology digraph of a preordered space, arXiv
T. Kahl, On the homology language of HDA models of transition systems, Journal of Applied and Computational Topology (2023), pdf available here
T. Kahl, On symmetric higher-dimensional automata and bisimilarity, Theoretical Computer Science 935 (2022), 47–60, pdf available here
T. Kahl, Weak equivalence of higher-dimensional automata, Discrete Mathematics and Theoretical Computer Science 23 (1) (2021), #12, 1–31, pdf
T. Kahl, Higher-dimensional automata modeling shared-variable systems, Logical Methods in Computer Science 15 (3) (2019), 28:1–28:21, pdf
T. Kahl, Labeled homology of higher-dimensional automata, Journal of Applied and Computational Topology 2 (3–4) (2018), 271–300, arXiv, accepted manuscript
T. Kahl, Topological abstraction of higher-dimensional automata, Theoretical Computer Science 631 (2016), 97–117, pdf available here
J. G. Carrasquel-Vera, T. Kahl, L. Vandembroucq, Rational approximations of sectional category and Poincaré duality, Proceedings of the American Mathematical Society 144 (2) (2016), 909–915, pdf
T. Kahl, The homology graph of a precubical set, Homology, Homotopy and Applications 16 (1) (2014), 119–138, pdf
T. Kahl, Weak morphisms of higher dimensional automata, Theoretical Computer Science 536 (2014), 42–61, pdf available here
T. Kahl, Some collapsing operations for 2-dimensional precubical sets, Journal of Homotopy and Related Structures 7 (2) (2012), 281–298, pdf available here
T. Kahl, A fibration category of local pospaces, Proceedings of the Workshops on Geometric and Topological Methods in Concurrency Theory (GETCO 2004+2005+2006), Electronic Notes in Theoretical Computer Science 230 (2009), 129–140, pdf available here
T. Kahl, H. Scheerer, D. Tanré, L. Vandembroucq, Simplicial resolutions and Ganea fibrations, Journal of Homotopy and Related Structures 3 (1) (2008), 309–330, pdf
T. Kahl, Note on L.-S. category and DGA modules, Bull. Belg. Math. Soc. 13 (2006), 703–717, pdf available here
T. Kahl, Relative directed homotopy theory of partially ordered spaces, Journal of Homotopy and Related Structures, vol. 1 (1) (2006), 79–100, pdf
T. Kahl, P. Lambrechts, L. Vandembroucq, Bords homotopiques et modèles de Quillen, Homology, Homotopy and Applications 8 (2) (2006), 1–28, pdf
L. Fernández Suárez, P. Ghienne, T. Kahl, L. Vandembroucq, Joins of DGA modules and sectional category, Algebraic & Geometric Topology 6 (2006), 119–144, pdf
T. Kahl, On the algebraic approximation of Lusternik-Schnirelmann category, J. Pure Appl. Algebra 181 (2003), 227–277, pdf available here
T. Kahl, L. Vandembroucq, Gaps in the Milnor-Moore spectral sequence, Bull. Belg. Math. Soc. 9 (2) (2002), 265–277, pdf available here
T. Kahl, LS-catégorie algébrique et attachement de cellules, Canad. Math. Bull. 44 (4) (2001), 459–468, pdf available here
T. Kahl, An axiomatic approach to Lusternik-Schnirelmann category type homotopy invariants, Rapp. Semin. Math. Louvain Nouv. Ser. 245–260, 224–253 (1996), pdf
Software
pg2hda - A tool to compute higher-dimensional automata modeling concurrent systems given by program graphs
Free software (MIT license). For information on installation and usage, see the included README file.
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