scientific article

Publication date: 17 September 1992

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

cohomology duality fundamental group projective spaces CW-complex singular homology homology theory covering spaces universal coefficient theorem compact surfaces cellular chain complex de Rham's theorem Künneth-formula Seifert-van Kampen's theorem

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Fundamental group, presentations, free differential calculus (57M05) Singular homology and cohomology theory (55N10) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology (55-01)

Related Items

Recursive Betti numbers for Cohen-Macaulay \(d\)-partite clutters arising from posets ⋮ On the contact boundaries of normal surface singularities ⋮ Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras ⋮ Algorithms to compute the topology of orientable real algebraic surfaces ⋮ Divisors on graphs, binomial and monomial ideals, and cellular resolutions ⋮ A geometric framework for sparse matrix problems ⋮ Homology and chaotic unfolding of chaos manifolds ⋮ Atiyah-Patodi-Singer \(\eta\)-invariant and invariants of finite degree ⋮ Simplicial dollar game ⋮ Simploidal sets: a data structure for handling simploidal Bézier spaces ⋮ Persistence of Morse decompositions over grid resolution for maps and time series ⋮ Manifolds that induce approximate fibrations in the PL category ⋮ Non-abelian vortices on surfaces and their statistics ⋮ The global medial structure of regions in \(\mathbb R^3\) ⋮ The Wall conjecture on domains in Euclidean spaces ⋮ On invariant domains in certain complex homogeneous spaces ⋮ Monotone homogeneity and planar manifolds with boundary ⋮ Time dependent periodic Navier-Stokes flows on a two-dimensional torus ⋮ On modular homology in the Boolean algebra. II ⋮ Independence number of graphs and line graphs of trees by means of omega invariant ⋮ LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies ⋮ Three approaches to Morse-Bott homology ⋮ 4-dimensional Busemann \(G\)-spaces are 4-manifolds ⋮ Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities ⋮ Charges and fluxes in Maxwell theory on compact manifolds with boundary ⋮ The cubical cohomology ring: an algorithmic approach ⋮ An algebraic method for computing \(N^\epsilon(f)\) ⋮ Classification of commutative zero-divisor semigroup graphs ⋮ Fixed point homomorphisms for parameterized maps ⋮ Real intersection homology ⋮ Computing cup products in \(\mathbb{Z}_2\)-cohomology of 3D polyhedral complexes ⋮ Foliation by graphs of CR mappings and a nonlinear Riemann-Hilbert problem for smoothly bounded domains ⋮ Homogeneous compact geometries ⋮ A combinatorial method for topology adaptations in 3D deformable models ⋮ Nielsen classes of orientation reversing homeomorphisms and complementary domains of plane separating invariant continua ⋮ Election in partially anonymous networks with arbitrary knowledge in message passing systems ⋮ Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes ⋮ Improved estimation of defocus blur and spatial shifts in spatial domain: A homotopy-based approach. ⋮ Galois coverings of pointed coalgebras. ⋮ Interlacing inequalities for eigenvalues of discrete Laplace operators ⋮ The lifting and classification problems for subspaces of covering spaces ⋮ Precise Arrhenius law for \(p\)-forms: the Witten Laplacian and Morse-Barannikov complex ⋮ Coreduction homology algorithm for regular CW-complexes ⋮ van Kampen theorems for toposes ⋮ A reduction of topological infinite-horizon optimization to periodic optimization in a class of compact 2-manifolds ⋮ Space complexity of perfect matching in bounded genus bipartite graphs ⋮ Covers of abelian varieties as analytic Zariski structures ⋮ Homology for higher-rank graphs and twisted \(C^*\)-algebras ⋮ On the optimal strategy for an isotropic blocking problem ⋮ Estimating trees from filtered data: identifiability of models for morphological phylogenetics ⋮ Sets of periods for maps on connected graphs with zero Euler characteristic having all branching points fixed ⋮ The orchard cocycle ⋮ \(T-\Omega\) formulation with higher-order hierarchical basis functions for nonsimply connected conductors ⋮ Global properties of integrable Hamiltonian systems ⋮ Statistical mechanics of vortices ⋮ On Borel fixed ideals generated in one degree ⋮ A new proposal for the picture changing operators in the minimal pure spinor formalism ⋮ The homotopy theory of Khovanov homology ⋮ Higher arithmetic intersection theory ⋮ Rigorous cubical approximation and persistent homology of continuous functions ⋮ On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions ⋮ A sharper estimate on the Betti numbers of sets defined by quadratic inequalities ⋮ Three-dimensional Alexandrov spaces with positive or nonnegative Ricci curvature ⋮ Pre-quantization of the moduli space of flat \(G\)-bundles over a surface ⋮ A survey of algebraic methods in digital topology. ⋮ A fundamental group for greyscale digital images ⋮ An isomorphism of motivic Galois groups ⋮ Cut-and-paste of quadriculated disks and arithmetic properties of the adjacency matrix ⋮ A foliated analogue of one- and two-dimensional Arakelov theory ⋮ Topological spaces associated to higher-rank graphs ⋮ Gauge orbit types for theories with gauge group \(O(n)\), \(SO(n)\) or \(Sp(n)\) ⋮ Denominator-preserving maps ⋮ A cubical model for a fibration ⋮ Computation of cubical homology, cohomology, and (co)homological operations via chain contraction ⋮ Five-coloring graphs on the Klein bottle ⋮ Computing pseudotriangulations via branched coverings ⋮ Character on a homogeneous space ⋮ A note on the structural stability of the equilibrium manifold ⋮ A simple and complete discrete exterior calculus on general polygonal meshes ⋮ The differentiable chain functor is not homotopy equivalent to the continuous chain functor ⋮ A geometrical procedure for computing relaxation ⋮ Bounds on sizes of finite bisimulations of Pfaffian dynamical systems ⋮ Generalized lattice gauge theory, spin foams and state sum invariants ⋮ The minimum speed for a blocking problem on the half plane ⋮ Desperately seeking mathematical proof ⋮ Graphs and their parallel groups ⋮ Spinning particles, braid groups and solitons ⋮ Long-time behavior of Navier-Stokes flow on a two-dimensional torus excited by an external sinusoidal force ⋮ A splitting theorem for transitive maps ⋮ On the capacity and depth of compact surfaces ⋮ Coincidence Nielsen numbers for covering maps for smooth manifolds ⋮ Self-homotopy equivalences which induce the identity on homology, cohomology or homotopy groups ⋮ Necessary conditions for feedback stabilization and safety ⋮ Approximation problems for curvature varifolds ⋮ The Bestvina-Edwards theorem and the Hilbert-Smith conjecture ⋮ Digital fundamental groups and edge groups of clique complexes ⋮ Local certification of graphs with bounded genus ⋮ An efficient algorithm for 1-dimensional (Persistent) path homology ⋮ The Reidemeister numbers and the Hirsch ranks for preimage subgroups ⋮ Euclidean symmetry of closed surfaces immersed in 3-space ⋮ GTED: Graph Traversal Edit Distance ⋮ Large N behaviour of the two-dimensional Yang–Mills partition function ⋮ Computing with Multi-membranes ⋮ Índice de Conley y sistemas dinámicos continuos ⋮ Characteristic-independence of Betti numbers of graph ideals ⋮ Digital homotopy relations and digital homology theories ⋮ Homogeneous weak solenoids ⋮ Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry ⋮ Puiseux parametric equations of analytic sets ⋮ Homeomorphic property of solutions of SDE driven by countably many Brownian motions with non-Lipschitzian coefficients ⋮ Algorithmical determination of the topology of a real algebraic surface ⋮ Molino theory for matchbox manifolds ⋮ -regularity of the Bergman projection on quotient domains ⋮ Incompressible solvable representations of surface groups ⋮ Preimage homomorphism indices of preimage classes ⋮ A multidimensional Birkhoff theorem for time-dependent Tonelli Hamiltonians ⋮ A new topology on the universal path space ⋮ A new approach to the automorphism group of a platonic surface ⋮ Cellular automorphisms and self-duality ⋮ Moduli spaces of lumps on real projective space ⋮ Unnamed Item ⋮ On the fractional NLS equation and the effects of the potential Well's topology ⋮ Partly Divisible Probability Measures on Locally Compact Abelian Groups ⋮ Decomposing Jacobians Via Galois covers ⋮ Discrete Morse functions and watersheds ⋮ Discrete cubical and path homologies of graphs ⋮ On somes characteristic classes of flat bundles in complex geometry ⋮ The Hurewicz theorem for cubical homology ⋮ Bergman kernels of two dimensional monomial polyhedra ⋮ Topological techniques in model selection ⋮ A homotopy-based approach for computing defocus blur and affine transform simultaneously ⋮ Knots, Diagrams and Kids’ Shoelaces. On Space and their Forms ⋮ Prescribing Morse Scalar Curvatures: Pinching and Morse Theory ⋮ On \(SL(2, \mathbb{C})\)-representations of torus knot groups ⋮ Chain duality for categories over complexes ⋮ The multidirectional Neumann problem in \(\mathbb R^{4}\) ⋮ Quotients of the square of a curve by a mixed action, further quotients and Albanese morphisms ⋮ Lectures on Klein Surfaces and Their Fundamental Group ⋮ Embeddings between partially commutative groups: two counterexamples. ⋮ Intersection space constructible complexes ⋮ Quasiflats in Hadamard spaces ⋮ Weakly well-composed cell complexes over nD pictures ⋮ Min-max theory and the Willmore conjecture ⋮ Unnamed Item ⋮ On the topology of foliations with a first integral ⋮ Homotopical variations and high-dimensional Zariski-van Kampen theorems ⋮ Three-manifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices ⋮ Wild solenoids ⋮ Unnamed Item ⋮ Geometry of the Aharonov-Bohm effect ⋮ Unnamed Item ⋮ The cut-off covering spectrum ⋮ A fundamental group for digital images ⋮ Computing the fundamental group of a higher-rank graph ⋮ Lectures on \(2\)D Yang-Mills theory, equivariant cohomology and topological field theories ⋮ Computational homotopy of finite regular CW-spaces ⋮ Graph Relabelling Systems ⋮ Variational formulae for Fuchsian groups over families of algebraic curves ⋮ Morse-Bott homology ⋮ Smooth gauge strings and \(D\geq 2\) lattice Yang-Mills theories ⋮ Rewriting systems for the surface classification theorem ⋮ Singular sources in gravity and homotopy in the space of connections ⋮ A presentation for the unipotent group over rings with identity ⋮ Indexing 3D Scenes Using the Interaction Bisector Surface ⋮ Shellability and regularity of chain complexes over a principal ideal domain ⋮ Measure homology and singular homology are isometrically isomorphic ⋮ A Markov partition that reflects the geometry of a hyperbolic toral automorphism ⋮ A multi-scale algorithm for drawing graphs nicely ⋮ Algorithms and complexity in biological pattern formation problems ⋮ An algorithmic approach to the construction of homomorphisms induced by maps in homology ⋮ The continuation of the Conley index for singular perturbations and the Conley indices in gradient-like systems. I ⋮ Homotopical complexity of a 3𝐷 billiard flow ⋮ Equivalent formulation and numerical analysis of a fire confinement problem ⋮ On the evolution of vector distance functions of closed curves ⋮ Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces ⋮ Cellular cohomology of posets with local coefficients ⋮ Universal covers for Hausdorff limits of noncompact spaces ⋮ An Inquiry into the Practice of Proving in Low-Dimensional Topology ⋮ A Framework for Component Categories ⋮ Holomorphic mappings of once-holed tori. II. ⋮ Digital Hurewicz theorem and digital homology theory ⋮ Puiseux Parametric Equations via the Amoeba of the Discriminant ⋮ On some incomplete theta integrals ⋮ Topology of exceptional orbit hypersurfaces of prehomogeneous spaces ⋮ On the universal cover and the fundamental group of an \(\mathsf{RCD}^\ast(K,N)\)-space ⋮ One More Step Towards Well-Composedness of Cell Complexes over nD Pictures ⋮ Non-uniqueness of weak solutions of the quantum-hydrodynamic system ⋮ Basic matrix perturbation theory ⋮ Moduli spaces of colored graphs ⋮ On the Vanishing of Discrete Singular Cubical Homology for Graphs ⋮ Optimal compatibility in systems markets ⋮ Connectedness criteria for graphs by means of omega invariant ⋮ Coverings of complexes of groups and developability ⋮ Computing fundamental groups from point clouds ⋮ Homology of cellular structures allowing multi-incidence

This page was built for publication: