Studying the first non-vanishing cohomology group of the Orlik-Solomon algebra for triangle-free graph related graphic arrangements
Résumé
In this work, we examine the vanishing of the second cohomology group of the Orlik- Solomon algebra , denoted by , corresponding to the graphic arrangement related with a triangle-free graph . Here, specifies the number of edges in and is defined as , for . Motivated by this goal, we investigate as a free module and show that it does not vanish when contains chordless 4-cycles including the edges and .
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Références
A. G. Fadhil and A. Hana’M, ”On the hypersolvable graphic arrangements,” A M. Sc. thesis submitted to College of Science/University of Basrah (2012).
E. Fadell and L. Neuwirth, ”CONFIGURATION SPACES,” Mathematica Scandinavica J., pp. 111-118, 1962, Accessed: Jan. 03, (2025). [Online]. Available: https://www.jstor.org/stable/24489273
R. Fox, L. N.-M. Scandinavica, and undefined 1962, ”The braid groups,” JSTORR Fox, L NeuwirthMathematica Scandinavica, 1962•JSTOR, Accessed: Jan. 03, (2025). [Online]. Available: https://www.jstor.org/stable/24489274
Y. Kawahara, ”The non-vanishing cohomology of orlik-solomon algebras,” Tokyo Journal of Mathematics, vol. 30, no. 1, (2007), pp. 223-238, doi: 10.3836/TJM/1184963658.
P. Orlik and H. Terao, Arrangements of hyperplanes, vol. 300. Springer Science & Business Media, (2013).
P. Orlik and L. Solomon, ”Combinatories and Topology of Complements of Hyperplanes,” Inventiones math, vol. 56, (1980), pp. 167-189, .
P. Orlik and H. Terao, ”Arrangements of Hyperplanes,” vol. 300, (1992), doi: 10.1007/978-3-662-02772-1.
S. Papadima and A. I. Suciu, ”Higher Homotopy Groups of Complements of Complex Hyperplane Arrangements,” Adv Math (N Y), vol. 165, no. 1, (2002), pp. 71-100, Jan. doi: 10.1006/AIMA.2001.2023.
S. Papadima and A. I. Suciu, ”Higher Homotopy Groups of Complements of Complex Hyperplane Arrangements,” Adv Math (N Y), vol. 165, no. 1, (2002) pp. 71-100, Jan. doi: 10.1006/AIMA.2001.2023.
K. J. Pearson, ”Cohomology of Orlik-Solomon algebras for quadratic arrangements.,” Lect. Mat., vol. 22, no. 2, (2001), pp. 103-134.
R. P. Stanley, ”Supersolvable lattices,” Algebra Universalis, vol. 2, no. 1, (1972) pp. 197-217, Dec. doi: https://doi.org/10.1007/BF02945028.
S. Yuzvinsky, ”Cohomology of the Brieskorn-Orlik-Solomon algebras,” 2006.
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