Studying the first non-vanishing cohomology group of the Orlik-Solomon algebra for triangle-free graph related graphic arrangements
DOI :
https://doi.org/10.5269/bspm.76788Résumé
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 .
Références
1. 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).
2. 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
3. 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
4. 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.
5. P. Orlik and H. Terao, Arrangements of hyperplanes, vol. 300. Springer Science & Business Media, (2013).
6. P. Orlik and L. Solomon, ”Combinatories and Topology of Complements of Hyperplanes,” Inventiones math, vol. 56, (1980), pp. 167-189, .
7. P. Orlik and H. Terao, ”Arrangements of Hyperplanes,” vol. 300, (1992), doi: 10.1007/978-3-662-02772-1.
8. 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.
9. 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.
10. K. J. Pearson, ”Cohomology of Orlik-Solomon algebras for quadratic arrangements.,” Lect. Mat., vol. 22, no. 2, (2001), pp. 103-134.
11. R. P. Stanley, ”Supersolvable lattices,” Algebra Universalis, vol. 2, no. 1, (1972) pp. 197-217, Dec. doi: https://doi.org/10.1007/BF02945028.
12. S. Yuzvinsky, ”Cohomology of the Brieskorn-Orlik-Solomon algebras,” 2006.
2. 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
3. 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
4. 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.
5. P. Orlik and H. Terao, Arrangements of hyperplanes, vol. 300. Springer Science & Business Media, (2013).
6. P. Orlik and L. Solomon, ”Combinatories and Topology of Complements of Hyperplanes,” Inventiones math, vol. 56, (1980), pp. 167-189, .
7. P. Orlik and H. Terao, ”Arrangements of Hyperplanes,” vol. 300, (1992), doi: 10.1007/978-3-662-02772-1.
8. 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.
9. 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.
10. K. J. Pearson, ”Cohomology of Orlik-Solomon algebras for quadratic arrangements.,” Lect. Mat., vol. 22, no. 2, (2001), pp. 103-134.
11. R. P. Stanley, ”Supersolvable lattices,” Algebra Universalis, vol. 2, no. 1, (1972) pp. 197-217, Dec. doi: https://doi.org/10.1007/BF02945028.
12. S. Yuzvinsky, ”Cohomology of the Brieskorn-Orlik-Solomon algebras,” 2006.
Téléchargements
Publié
2025-07-29
Numéro
Rubrique
Research Articles
Licence
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
