Combinatorial Morse theory and minimality of hyperplane arrangements

DOI10.2140/gt.2007.11.1733zbMath1134.32010arXiv0705.2874OpenAlexW1979882439MaRDI QIDQ2464834

Simona Settepanella, Mario Salvetti

Publication date: 17 December 2007

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.2874

zbMATH Keywords

arrangementscombinatoricsMorse theory

Mathematics Subject Classification ID

Relations with arrangements of hyperplanes (32S22) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants (32S50)

Related Items

Semi-algebraic partition and basis of Borel-Moore homology of hyperplane arrangements ⋮ Homology graph of real arrangements and monodromy of Milnor fiber ⋮ Discrete Morse theory and classifying spaces ⋮ Divides with cusps and Kirby diagrams for line arrangements ⋮ Combinatorial polar orderings and recursively orderable arrangements ⋮ Unnamed Item ⋮ Combinatorial Stratifications and Minimality of Two-Arrangements ⋮ Recent topics of arrangements of hyperplanes ⋮ Combinatorial stratifications and minimality of 2-arrangements ⋮ Collapsibility of CAT(0) spaces ⋮ On the homology of the real complement of the \(k\)-parabolic subspace arrangement ⋮ On the Twisted Cohomology of Affine Line Arrangements ⋮ Some computations on the characteristic variety of a line arrangement ⋮ Discrete Morse theory and a reformulation of theK(π,1)-conjecture ⋮ Euclidean matchings and minimality of hyperplane arrangements ⋮ Computing Milnor fiber monodromy for some projective hypersurfaces ⋮ Configuration spaces of disks in an infinite strip ⋮ The homotopy type of the complement to a system of complex lines in \(\mathbb C^2\) ⋮ Moment-angle complexes of pairs \((D^n,S^{n-1})\) and simplicial complexes with vertex-decomposable duals ⋮ Minimality of toric arrangements ⋮ The Morse complex of a line arrangement ⋮ Factorization statistics and bug-eyed configuration spaces ⋮ The chamber basis of the Orlik-Solomon algebra and Aomoto complex

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topology of the complement of real hyperplanes in \({\mathbb C}^ N\)
• Homology of a local system on the complement of hyperplanes
• Morse theory for cell complexes
• A user's guide to discrete Morse theory
• Hypersurface complements, Milnor fibers and higher homotopy groups of arrangements
• Arrangements and local systems
• Cohomology of local systems on the complement of hyperplanes
• Cohomology and intersection cohomology of complex hyperplane arrangements
• Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
• The homotopy type of Artin groups
• Hyperplane arrangements and Lefschetz's hyperplane section theorem
• Cohomologies of the group COS mod 2
• Combinatorial Stratification of Complex Arrangements
• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• Morse theory, Milnor fibers and minimality of hyperplane arrangements
• Translated tori in the characteristic varieties of complex hyperplane arrangements