The topology of Helmholtz domains

DOI10.1016/j.exmath.2012.09.001zbMath1276.57001arXiv1001.4418OpenAlexW2963784701MaRDI QIDQ1931418

Roberto Frigerio, Riccardo Benedetti, Riccardo Ghiloni

Publication date: 14 January 2013

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4418

zbMATH Keywords

Hodge decompositioncorankcut numberhomology boundary linkmethod of cutting surfaces

Mathematics Subject Classification ID

Related Items (13)

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Cites Work

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• On Dehn's lemma and the asphericity of knots
• Homology boundary links and the Andrews-Curtis conjecture
• Moves and invariants for knotted handlebodies
• A la recherche de la topologie perdue. 1: Du côté de chez Rohlin. 2: Le côté de Casson
• A geometric proof that boundary links are homotopically trivial
• Detecting unknotted graphs in 3-space
• Is a knotted graph determined by its associated links?
• Thin position and Heegaard splittings of the 3-sphere
• Cobordism, homotopy and homology of graphs in \(\mathbb{R}^ 3\)
• Homology boundary links and Blanchfield forms: Concordance classification and new tangle-theoretic constructions
• Homology classification of spatial graphs by linking numbers and Simon invariants
• Invariants of theta-curves and other graphs in 3-space
• On the cut number of a \(3\)-manifold
• Alexander ideals of graphs in the 3-sphere
• Hodge decomposition for symmetric matrix fields and the elasticity complex in Lipschitz domains
• Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
• Heegaard-Zerlegungen der 3-Sphäre
• Mapping cubes with holes onto cubes with handles
• Nonretractable cubes-with-holes
• Retracting three-manifolds onto finite graphs
• On elementary ideals of polyhedra in the 3-sphere
• On the imbedding of polyhedra in 3-space
• Locally tame sets are tame
• Link groups
• Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds
• Levels of knotting of spatial handlebodies
• Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems
• Quandle Cocycle Invariants for Spatial Graphs and Knotted Handlebodies
• Derivatives of links: Milnor’s concordance invariants and Massey’s products
• Homotopy on spatial graphs and the Sato-Levine invariant
• BOUNDARY LINKS ARE HOMOTOPY TRIVIAL
• Invariants of Graphs in Three-Space
• Magnetostatic and Electrostatic Problems in Inhomogeneous Anisotropic Media with Irregular Boundary and Mixed Boundary Conditions
• Morse Theory. (AM-51)
• Milnor's &   956; -Invariants and Massey Products
• Link Cobordism and Milnor's Invariant
• Differential Topology
• Vector potentials in three-dimensional non-smooth domains
• Vector Calculus and the Topology of Domains in 3-Space
• SEIFERT SURFACES FOR GRAPHS
• Cut numbers of 3-manifolds
• A Finite Element Method with Lagrange Multipliers for Low-Frequency Harmonic Maxwell Equations
• Electromagnetic Theory and Computation
• Boundary Links and an Unlinking Theorem
• Not all links are concordant to boundary links
• Locally flat imbeddings of topological manifolds

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