Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Homology_(mathematics)> ?p ?o }
- Homology_(mathematics) abstract "In mathematics (especially algebraic topology and abstract algebra), homology (in part from Greek ὁμός homos \"identical\") is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. However, similar constructions are available in a wide variety of other contexts, such as groups, Lie algebras, Galois theory, and algebraic geometry.The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is \"not there\", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for defining and categorizing holes in a manifold. Loosely speaking, a cycle is a closed submanifold, a boundary is the boundary of a submanifold with boundary, and a homology class (which represents a hole) is an equivalence class of cycles modulo boundaries.There are many different homology theories. A particular type of mathematical object, such as a topological space or a group, may have one or more associated homology theories. When the underlying object has a geometric interpretation like topological spaces do, the nth homology group represents behavior unique to dimension n. In general, most homology groups or modules arise as derived functors on appropriate abelian categories. They provide concrete descriptions of the failure of a functor to be exact. From this abstract perspective, homology groups are determined by objects of a derived category.".
- Homology_(mathematics) thumbnail Spherecycles1.svg?width=300.
- Homology_(mathematics) wikiPageExternalLink chomp.rutgers.edu.
- Homology_(mathematics) wikiPageExternalLink linalg.org.
- Homology_(mathematics) wikiPageExternalLink redhom.ii.uj.edu.pl.
- Homology_(mathematics) wikiPageExternalLink 1361982.
- Homology_(mathematics) wikiPageExternalLink 529171.
- Homology_(mathematics) wikiPageExternalLink Kenzo.
- Homology_(mathematics) wikiPageExternalLink Homology_group.
- Homology_(mathematics) wikiPageExternalLink www.gap-system.org.
- Homology_(mathematics) wikiPageExternalLink www.maplesoft.com.
- Homology_(mathematics) wikiPageExternalLink ATchapters.html.
- Homology_(mathematics) wikiPageExternalLink survey.pdf.
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- Homology_(mathematics) wikiPageWikiLink Abelian_category.
- Homology_(mathematics) wikiPageWikiLink Abelian_group.
- Homology_(mathematics) wikiPageWikiLink Abstract_algebra.
- Homology_(mathematics) wikiPageWikiLink Algebraic_geometry.
- Homology_(mathematics) wikiPageWikiLink Algebraic_topology.
- Homology_(mathematics) wikiPageWikiLink Algebraic_variety.
- Homology_(mathematics) wikiPageWikiLink American_Mathematical_Society.
- Homology_(mathematics) wikiPageWikiLink Analysis_Situs_(paper).
- Homology_(mathematics) wikiPageWikiLink Antipodal_point.
- Homology_(mathematics) wikiPageWikiLink Ball_(mathematics).
- Homology_(mathematics) wikiPageWikiLink Bar-Ilan_University.
- Homology_(mathematics) wikiPageWikiLink Betti_number.
- Homology_(mathematics) wikiPageWikiLink Borel–Moore_homology.
- Homology_(mathematics) wikiPageWikiLink Borsuk–Ulam_theorem.
- Homology_(mathematics) wikiPageWikiLink Boundary_value_problem.
- Homology_(mathematics) wikiPageWikiLink Boys_surface.
- Homology_(mathematics) wikiPageWikiLink Braid_theory.
- Homology_(mathematics) wikiPageWikiLink Brouwer_fixed-point_theorem.
- Homology_(mathematics) wikiPageWikiLink C++.
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- Homology_(mathematics) wikiPageWikiLink Category:Homology_theory.
- Homology_(mathematics) wikiPageWikiLink Category_(mathematics).
- Homology_(mathematics) wikiPageWikiLink Cellular_homology.
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- Homology_(mathematics) wikiPageWikiLink Circle.
- Homology_(mathematics) wikiPageWikiLink Cohomology.
- Homology_(mathematics) wikiPageWikiLink Combinatorial_topology.
- Homology_(mathematics) wikiPageWikiLink Computational_electromagnetics.
- Homology_(mathematics) wikiPageWikiLink Connected_space.
- Homology_(mathematics) wikiPageWikiLink Connected_sum.
- Homology_(mathematics) wikiPageWikiLink Continuous_function.
- Homology_(mathematics) wikiPageWikiLink Contractible_space.
- Homology_(mathematics) wikiPageWikiLink Cross-cap.
- Homology_(mathematics) wikiPageWikiLink Cycle_space.
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- Homology_(mathematics) wikiPageWikiLink Derived_category.
- Homology_(mathematics) wikiPageWikiLink Derived_functor.
- Homology_(mathematics) wikiPageWikiLink Dimension_(vector_space).
- Homology_(mathematics) wikiPageWikiLink Discrete_Morse_theory.
- Homology_(mathematics) wikiPageWikiLink Dynamical_system.
- Homology_(mathematics) wikiPageWikiLink Eilenberg–Steenrod_axioms.
- Homology_(mathematics) wikiPageWikiLink Emmy_Noether.
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- Homology_(mathematics) wikiPageWikiLink Euler_characteristic.
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- Homology_(mathematics) wikiPageWikiLink Finite_element_method.
- Homology_(mathematics) wikiPageWikiLink Finitely_generated_abelian_group.
- Homology_(mathematics) wikiPageWikiLink Floer_homology.
- Homology_(mathematics) wikiPageWikiLink Free_abelian_group.
- Homology_(mathematics) wikiPageWikiLink Functor.
- Homology_(mathematics) wikiPageWikiLink Galois_theory.
- Homology_(mathematics) wikiPageWikiLink Generating_set_of_a_group.
- Homology_(mathematics) wikiPageWikiLink Genus_(mathematics).
- Homology_(mathematics) wikiPageWikiLink Gmsh.
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- Homology_(mathematics) wikiPageWikiLink Greek_language.
- Homology_(mathematics) wikiPageWikiLink Group_(mathematics).
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- Homology_(mathematics) wikiPageWikiLink Hairy_ball_theorem.
- Homology_(mathematics) wikiPageWikiLink Henri_Cartan.
- Homology_(mathematics) wikiPageWikiLink Henri_Poincaré.
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- Homology_(mathematics) wikiPageWikiLink Homeomorphism.
- Homology_(mathematics) wikiPageWikiLink Homological_algebra.
- Homology_(mathematics) wikiPageWikiLink Homological_conjectures_in_commutative_algebra.
- Homology_(mathematics) wikiPageWikiLink Homological_dimension.
- Homology_(mathematics) wikiPageWikiLink Homotopy.
- Homology_(mathematics) wikiPageWikiLink Image_(mathematics).
- Homology_(mathematics) wikiPageWikiLink Injective_function.
- Homology_(mathematics) wikiPageWikiLink Intersection_homology.
- Homology_(mathematics) wikiPageWikiLink Invariance_of_domain.
- Homology_(mathematics) wikiPageWikiLink Invariant_manifold.
- Homology_(mathematics) wikiPageWikiLink John_Stillwell.
- Homology_(mathematics) wikiPageWikiLink Jordan_curve_theorem.
- Homology_(mathematics) wikiPageWikiLink K-homology.
- Homology_(mathematics) wikiPageWikiLink Kernel_(algebra).
- Homology_(mathematics) wikiPageWikiLink Khovanov_homology.
- Homology_(mathematics) wikiPageWikiLink Klein_bottle.
- Homology_(mathematics) wikiPageWikiLink Kolmogorov–Arnold–Moser_theorem.
- Homology_(mathematics) wikiPageWikiLink Künneth_theorem.
- Homology_(mathematics) wikiPageWikiLink Laplace_operator.