Algebraic & Geometric Topology Volume 24, issue 8 (2024)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Multipath cohomology of directed graphs

Luigi Caputi, Carlo Collari and Sabino Di Trani

Algebraic & Geometric Topology 24 (2024) 4373–4421

DOI: 10.2140/agt.2024.24.4373

Bibliography

1	R Aharoni, E Berger, R Meshulam, Eigenvalues and homology of flag complexes and vector representations of graphs, Geom. Funct. Anal. 15 (2005) 555 MR2221142
2	A Björner, Posets, regular CW complexes and Bruhat order, European J. Combin. 5 (1984) 7 MR746039
3	L Caputi, A Pidnebesna, J Hlinka, Promises and pitfalls of topological data analysis for brain connectivity analysis, NeuroImage 238 (2021) 118245
4	L Caputi, C Collari, S Di Trani, Combinatorial and topological aspects of path posets, and multipath cohomology, J. Algebraic Combin. 57 (2023) 617 MR4570416
5	L Caputi, D Celoria, C Collari, Monotone cohomologies and oriented matchings, Homology Homotopy Appl. 26 (2024) 137
6	L Caputi, C Collari, S Di Trani, J P Smith, On the homotopy type of multipath complexes, Mathematika 70 (2024) MR4687754
7	A Chandler, Thin posets, CW posets, and categorification, preprint (2019) arXiv:1911.05600
8	B Chen, S T Yau, Y N Yeh, Graph homotopy and Graham homotopy, Discrete Math. 241 (2001) 153 MR1861415
9	M Chmutov, S Chmutov, Y Rong, Knight move in chromatic cohomology, European J. Combin. 29 (2008) 311 MR2368638
10	H Edelsbrunner, D Letscher, A Zomorodian, Topological persistence and simplification, Discrete Comput. Geom. 28 (2002) 511 MR1949898
11	B Everitt, P Turner, Homology of coloured posets : a generalisation of Khovanov’s cube construction, J. Algebra 322 (2009) 429 MR2529096
12	B Everitt, P Turner, Cellular cohomology of posets with local coefficients, J. Algebra 439 (2015) 134 MR3373367
13	P Gabriel, M Zisman, Calculus of fractions and homotopy theory, 35, Springer (1967) MR210125
14	D Govc, R Levi, J P Smith, Complexes of tournaments, directionality filtrations and persistent homology, J. Appl. Comput. Topol. 5 (2021) 313 MR4259436
15	A A Grigoryan, Y Lin, Y V Muranov, S Yau, Path complexes and their homologies, Fundam. Prikl. Mat. 21 (2016) 79 MR3845076
16	D Happel, Hochschild cohomology of finite-dimensional algebras, from: "Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin", Lecture Notes in Math. 1404, Springer (1989) 108 MR1035222
17	L Helme-Guizon, Y Rong, A categorification for the chromatic polynomial, Algebr. Geom. Topol. 5 (2005) 1365 MR2171813
18	A V Ivashchenko, Contractible transformations do not change the homology groups of graphs, Discrete Math. 126 (1994) 159 MR1264484
19	J Jonsson, Simplicial complexes of graphs, 1928, Springer (2008) MR2368284
20	M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
21	D Kozlov, Combinatorial algebraic topology, 21, Springer (2008) MR2361455
22	E S Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005) 554 MR2173845
23	J L Loday, Cyclic homology, 301, Springer (1992) MR1217970
24	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
25	S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR354798
26	T Nikolaus, P Scholze, On topological cyclic homology, Acta Math. 221 (2018) 203 MR3904731
27	J H Przytycki, When the theories meet : Khovanov homology as Hochschild homology of links, Quantum Topol. 1 (2010) 93 MR2657644
28	K K Putyra, A 2–category of chronological cobordisms and odd Khovanov homology, from: "Knots in Poland, III : Part 3", Banach Center Publ. 103, Polish Acad. Sci. Inst. Math. (2014) 291 MR3363817
29	D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR338129
30	D Quillen, Homotopy properties of the poset of nontrivial p–subgroups of a group, Adv. Math. 28 (1978) 101 MR493916
31	J E Roos, Sur les foncteurs dérivés de : applications, C. R. Acad. Sci. Paris 252 (1961) 3702 MR132091
32	P Turner, E Wagner, The homology of digraphs as a generalization of Hochschild homology, J. Algebra Appl. 11 (2012) 1250031 MR2925445
33	M L Wachs, Topology of matching, chessboard, and general bounded degree graph complexes, Algebra Universalis 49 (2003) 345 MR2022345
34	D B West, Introduction to graph theory, Prentice Hall (1996) MR1367739
35	A Zomorodian, G Carlsson, Computing persistent homology, Discrete Comput. Geom. 33 (2005) 249 MR2121296