电邮这篇文章 Connection between coordinate and diagonal arrangement complements
- 作者: Tril V.A.1,2
-
隶属关系:
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
- 期: 卷 216, 编号 11 (2025)
- 页面: 150-166
- 栏目: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/351339
- DOI: https://doi.org/10.4213/sm10222
- ID: 351339
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详细
We study diagonal arrangement complements $D(\mathcal K)$ in $\mathbb C^m$ . We consider the class of simplicial complexes $\mathcal K$ in which any two missing faces have a common vertex, and we prove that the coordinate arrangement complement $U(\mathcal K)$ is the double suspension of the diagonal arrangement complement $D(\mathcal K)$ . In the case of subspace arrangements in $\mathbb R^m$ the coordinate arrangement complement $U_{\mathbb R}(\mathcal K)$ is the single suspension of $D_{\mathbb R}(\mathcal K)$ .
作者简介
Vsevolod Tril
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia; Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Email: vsevolod.tril@math.msu.ru
ORCID iD: 0009-0004-6431-2211
without scientific degree, no status
参考
- A. Ayzenberg, “Buchstaber invariant, minimal non-simplices and related”, Osaka J. Math., 53:2 (2016), 377–395
- A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler, “The polyhedral product functor: a method of decomposition for moment-angle complexes, arrangements and related spaces”, Adv. Math., 225:3 (2010), 1634–1668
- A. Björner, L. Lovasz, “Linear decision trees, subspace arrangements, and Möbius functions”, J. Amer. Math. Soc., 7:3 (1994), 677–706
- A. Björner, V. Welker, “The homology of “$k$-equal” manifolds and related partition lattices”, Adv. Math., 110:2 (1995), 277–313
- A. Björner, G. M. Ziegler, “Combinatorial stratification of complex arrangements”, J. Amer. Math. Soc., 5:1 (1992), 105–149
- V. M. Buchstaber, T. E. Panov, Toric topology, Math. Surveys Monogr., 204, Amer. Math. Soc., Providence, RI, 2015, xiv+518 pp.
- N. Dobrinskaya, Loops on polyhedral products and diagonal arrangements
- M. Goresky, R. MacPherson, Stratified Morse theory, Ergeb. Math. Grenzgeb. (3), 14, Springer-Verlag, Berlin, 1988, xiv+272 pp.
- J. Grbic, T. Panov, S. Theriault, Jie Wu, “The homotopy types of moment-angle complexes for flag complexes”, Trans. Amer. Math. Soc., 368:9 (2016), 6663–6682
- J. Grbic, S. Theriault, “The homotopy type of the complement of a coordinate subspace arrangement”, Topology, 46:4 (2007), 357–396
- K. Iriye, D. Kishimoto, “Fat-wedge filtration and decomposition of polyhedral products”, Kyoto J. Math., 59:1 (2019), 1–51
- M. de Longueville, C. A. Schultz, “The cohomology rings of complements of subspace arrangements”, Math. Ann., 319:4 (2001), 625–646
- T. Panov, V. Tril, Permutohedral complex and complements of diagonal subspace arrangements
- I. Peeva, V. Reiner, V. Welker, “Cohomology of real diagonal subspace arrangements via resolutions”, Compositio Math., 117:1 (1999), 99–115
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