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- Simplicial_homology abstract "In algebraic topology, simplicial homology formalizes the idea of the number of holes of a given dimension in a simplicial complex. This generalizes the number of connected components (the case of dimension 0).Simplicial homology arose as a way to study topological spaces whose building blocks are n-simplices, the n-dimensional analogs of triangles. This includes a point (0-dimensional simplex), a line segment (1-dimensional simplex), a triangle (2-dimensional simplex) and a tetrahedron (3-dimensional simplex). By definition, such a space is homeomorphic to a simplicial complex (more precisely, the geometric realization of an abstract simplicial complex). Such a homeomorphism is referred to as a triangulation of the given space. Many topological spaces of interest can be triangulated, including every smooth manifold, by Cairns and Whitehead.Simplicial homology is defined by a simple recipe for any abstract simplicial complex. It is a remarkable fact that simplicial homology only depends on the associated topological space. As a result, it gives a computable way to distinguish one space from another.Singular homology is a related theory which is more commonly used by mathematicians today. Singular homology is defined for all topological spaces, and it agrees with simplicial homology for spaces which can be triangulated. Nonetheless, because it is possible to compute the simplicial homology of a simplicial complex automatically and efficiently, simplicial homology has become important for application to real-life situations, such as image analysis, medical imaging, and data analysis in general.".
- Simplicial_homology thumbnail Simplicial_homology_-_exactness_of_boundary_maps.svg?width=300.
- Simplicial_homology wikiPageExternalLink ATchapters.html.
- Simplicial_homology wikiPageExternalLink 28.htm.
- Simplicial_homology wikiPageExternalLink paper.php?id=elz-tps-02.
- Simplicial_homology wikiPageExternalLink comptop.
- Simplicial_homology wikiPageExternalLink programs.
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- Simplicial_homology wikiPageExternalLink dionysus.
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- Simplicial_homology wikiPageID "1060236".
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- Simplicial_homology wikiPageWikiLink Abstract_simplicial_complex.
- Simplicial_homology wikiPageWikiLink Algebraic_topology.
- Simplicial_homology wikiPageWikiLink American_Mathematical_Society.
- Simplicial_homology wikiPageWikiLink Betti_number.
- Simplicial_homology wikiPageWikiLink Brouwer_fixed-point_theorem.
- Simplicial_homology wikiPageWikiLink Brouwer_fixed_point_theorem.
- Simplicial_homology wikiPageWikiLink C++.
- Simplicial_homology wikiPageWikiLink Cambridge_University_Press.
- Simplicial_homology wikiPageWikiLink Category:Algebraic_topology.
- Simplicial_homology wikiPageWikiLink Category:Computational_topology.
- Simplicial_homology wikiPageWikiLink Category:Homology_theory.
- Simplicial_homology wikiPageWikiLink Cellular_homology.
- Simplicial_homology wikiPageWikiLink Chain_(algebraic_topology).
- Simplicial_homology wikiPageWikiLink Chain_complex.
- Simplicial_homology wikiPageWikiLink Chain_map.
- Simplicial_homology wikiPageWikiLink Connected_component_(topology).
- Simplicial_homology wikiPageWikiLink Connected_space.
- Simplicial_homology wikiPageWikiLink Data_analysis.
- Simplicial_homology wikiPageWikiLink Data_mining.
- Simplicial_homology wikiPageWikiLink Even_permutation.
- Simplicial_homology wikiPageWikiLink File:Triangles_for_simplical_homology.jpg.
- Simplicial_homology wikiPageWikiLink Free_abelian_group.
- Simplicial_homology wikiPageWikiLink Functor.
- Simplicial_homology wikiPageWikiLink Geometric_realization.
- Simplicial_homology wikiPageWikiLink Gunnar_Carlsson.
- Simplicial_homology wikiPageWikiLink Homeomorphic.
- Simplicial_homology wikiPageWikiLink Homeomorphism.
- Simplicial_homology wikiPageWikiLink Homology_(mathematics).
- Simplicial_homology wikiPageWikiLink Homology_theory.
- Simplicial_homology wikiPageWikiLink Homomorphism.
- Simplicial_homology wikiPageWikiLink Image_analysis.
- Simplicial_homology wikiPageWikiLink J.H.C._Whitehead.
- Simplicial_homology wikiPageWikiLink J._H._C._Whitehead.
- Simplicial_homology wikiPageWikiLink MATLAB.
- Simplicial_homology wikiPageWikiLink Manifold.
- Simplicial_homology wikiPageWikiLink Medical_imaging.
- Simplicial_homology wikiPageWikiLink Orientability.
- Simplicial_homology wikiPageWikiLink Parity_of_a_permutation.
- Simplicial_homology wikiPageWikiLink Persistent_homology.
- Simplicial_homology wikiPageWikiLink Quotient_group.
- Simplicial_homology wikiPageWikiLink Rank_of_an_abelian_group.
- Simplicial_homology wikiPageWikiLink Simplex.
- Simplicial_homology wikiPageWikiLink Simplices.
- Simplicial_homology wikiPageWikiLink Simplicial_complex.
- Simplicial_homology wikiPageWikiLink Simplicial_set.
- Simplicial_homology wikiPageWikiLink Singular_homology.
- Simplicial_homology wikiPageWikiLink Springer-Verlag.
- Simplicial_homology wikiPageWikiLink Springer_Science+Business_Media.
- Simplicial_homology wikiPageWikiLink Topological_data_analysis.
- Simplicial_homology wikiPageWikiLink Topological_space.
- Simplicial_homology wikiPageWikiLink Topological_spaces.
- Simplicial_homology wikiPageWikiLink Triangulation_(topology).
- Simplicial_homology wikiPageWikiLink Vin_de_Silva.
- Simplicial_homology wikiPageWikiLink File:Simplicial_homology_-_exactness_of_boundary_maps.svg.
- Simplicial_homology wikiPageWikiLinkText "Homology".
- Simplicial_homology wikiPageWikiLinkText "Simplicial homology".
- Simplicial_homology wikiPageWikiLinkText "simplicial (co)homology".
- Simplicial_homology wikiPageWikiLinkText "simplicial chain complex".
- Simplicial_homology wikiPageWikiLinkText "simplicial cohomology".
- Simplicial_homology wikiPageWikiLinkText "simplicial homology".
- Simplicial_homology wikiPageWikiLinkText "simplicial".
- Simplicial_homology hasPhotoCollection Simplicial_homology.
- Simplicial_homology wikiPageUsesTemplate Template:Citation.
- Simplicial_homology wikiPageUsesTemplate Template:Reflist.
- Simplicial_homology subject Category:Algebraic_topology.
- Simplicial_homology subject Category:Computational_topology.
- Simplicial_homology subject Category:Homology_theory.
- Simplicial_homology comment "In algebraic topology, simplicial homology formalizes the idea of the number of holes of a given dimension in a simplicial complex. This generalizes the number of connected components (the case of dimension 0).Simplicial homology arose as a way to study topological spaces whose building blocks are n-simplices, the n-dimensional analogs of triangles.".
- Simplicial_homology label "Simplicial homology".
- Simplicial_homology sameAs Simpliziale_Homologie.
- Simplicial_homology sameAs m.025rq0c.
- Simplicial_homology sameAs Q7520902.
- Simplicial_homology sameAs Q7520902.
- Simplicial_homology wasDerivedFrom Simplicial_homology?oldid=669577402.
- Simplicial_homology depiction Simplicial_homology_-_exactness_of_boundary_maps.svg.
- Simplicial_homology isPrimaryTopicOf Simplicial_homology.