Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Mayer–Vietoris_sequence> ?p ?o }
- Mayer–Vietoris_sequence abstract "In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to two Austrian mathematicians, Walther Mayer and Leopold Vietoris. The method consists of splitting a space into subspaces, for which the homology or cohomology groups may be easier to compute. The sequence relates the (co)homology groups of the space to the (co)homology groups of the subspaces. It is a natural long exact sequence, whose entries are the (co)homology groups of the whole space, the direct sum of the (co)homology groups of the subspaces, and the (co)homology groups of the intersection of the subspaces.The Mayer–Vietoris sequence holds for a variety of cohomology and homology theories, including singular homology and singular cohomology. In general, the sequence holds for those theories satisfying the Eilenberg–Steenrod axioms, and it has variations for both reduced and relative (co)homology. Because the (co)homology of most spaces cannot be computed directly from their definitions, one uses tools such as the Mayer–Vietoris sequence in the hope of obtaining partial information. Many spaces encountered in topology are constructed by piecing together very simple patches. Carefully choosing the two covering subspaces so that, together with their intersection, they have simpler (co)homology than that of the whole space may allow a complete deduction of the (co)homology of the space. In that respect, the Mayer–Vietoris sequence is analogous to the Seifert–van Kampen theorem for the fundamental group, and a precise relation exists for homology of dimension one.".
- Mayer–Vietoris_sequence thumbnail Vietoris4343.jpg?width=300.
- Mayer–Vietoris_sequence wikiPageExternalLink fea-vietoris.pdf.
- Mayer–Vietoris_sequence wikiPageExternalLink ATpage.html.
- Mayer–Vietoris_sequence wikiPageExternalLink x33611021p942518.
- Mayer–Vietoris_sequence wikiPageID "378677".
- Mayer–Vietoris_sequence wikiPageLength "24772".
- Mayer–Vietoris_sequence wikiPageOutDegree "141".
- Mayer–Vietoris_sequence wikiPageRevisionID "646561244".
- Mayer–Vietoris_sequence wikiPageWikiLink 0-sphere.
- Mayer–Vietoris_sequence wikiPageWikiLink Algebra.
- Mayer–Vietoris_sequence wikiPageWikiLink Algebraic_invariant.
- Mayer–Vietoris_sequence wikiPageWikiLink Algebraic_topology.
- Mayer–Vietoris_sequence wikiPageWikiLink American_Mathematical_Society.
- Mayer–Vietoris_sequence wikiPageWikiLink Austria.
- Mayer–Vietoris_sequence wikiPageWikiLink Bar-Ilan_University.
- Mayer–Vietoris_sequence wikiPageWikiLink Barycentric_subdivision.
- Mayer–Vietoris_sequence wikiPageWikiLink Basepoint.
- Mayer–Vietoris_sequence wikiPageWikiLink Betti_number.
- Mayer–Vietoris_sequence wikiPageWikiLink CW_complex.
- Mayer–Vietoris_sequence wikiPageWikiLink Cambridge_University_Press.
- Mayer–Vietoris_sequence wikiPageWikiLink Category:Homology_theory.
- Mayer–Vietoris_sequence wikiPageWikiLink Category_(mathematics).
- Mayer–Vietoris_sequence wikiPageWikiLink Chain_complex.
- Mayer–Vietoris_sequence wikiPageWikiLink Chain_group.
- Mayer–Vietoris_sequence wikiPageWikiLink Closed_and_exact_differential_forms.
- Mayer–Vietoris_sequence wikiPageWikiLink Cobordism.
- Mayer–Vietoris_sequence wikiPageWikiLink Cohomology.
- Mayer–Vietoris_sequence wikiPageWikiLink Cohomology_group.
- Mayer–Vietoris_sequence wikiPageWikiLink Cohomology_theory.
- Mayer–Vietoris_sequence wikiPageWikiLink Commutative_diagram.
- Mayer–Vietoris_sequence wikiPageWikiLink Commutator_subgroup.
- Mayer–Vietoris_sequence wikiPageWikiLink Complement_(set_theory).
- Mayer–Vietoris_sequence wikiPageWikiLink Connected_space.
- Mayer–Vietoris_sequence wikiPageWikiLink Continuous_function.
- Mayer–Vietoris_sequence wikiPageWikiLink Continuous_function_(topology).
- Mayer–Vietoris_sequence wikiPageWikiLink Contractible.
- Mayer–Vietoris_sequence wikiPageWikiLink Contractible_space.
- Mayer–Vietoris_sequence wikiPageWikiLink Cover_(topology).
- Mayer–Vietoris_sequence wikiPageWikiLink De_Rham_cohomology.
- Mayer–Vietoris_sequence wikiPageWikiLink Deformation_retract.
- Mayer–Vietoris_sequence wikiPageWikiLink Differentiable_manifold.
- Mayer–Vietoris_sequence wikiPageWikiLink Differential_form.
- Mayer–Vietoris_sequence wikiPageWikiLink Dimension_axiom.
- Mayer–Vietoris_sequence wikiPageWikiLink Direct_sum.
- Mayer–Vietoris_sequence wikiPageWikiLink Direct_sum_of_abelian_groups.
- Mayer–Vietoris_sequence wikiPageWikiLink Duality_(mathematics).
- Mayer–Vietoris_sequence wikiPageWikiLink Eilenberg–Steenrod_axioms.
- Mayer–Vietoris_sequence wikiPageWikiLink Empty_set.
- Mayer–Vietoris_sequence wikiPageWikiLink Exact_sequence.
- Mayer–Vietoris_sequence wikiPageWikiLink Excision_theorem.
- Mayer–Vietoris_sequence wikiPageWikiLink Extraordinary_cohomology_theories.
- Mayer–Vietoris_sequence wikiPageWikiLink Fundamental_group.
- Mayer–Vietoris_sequence wikiPageWikiLink Group_(mathematics).
- Mayer–Vietoris_sequence wikiPageWikiLink Group_homomorphism.
- Mayer–Vietoris_sequence wikiPageWikiLink Homeomorphic.
- Mayer–Vietoris_sequence wikiPageWikiLink Homeomorphism.
- Mayer–Vietoris_sequence wikiPageWikiLink Homological_algebra.
- Mayer–Vietoris_sequence wikiPageWikiLink Homology_(mathematics).
- Mayer–Vietoris_sequence wikiPageWikiLink Homology_group.
- Mayer–Vietoris_sequence wikiPageWikiLink Homology_theory.
- Mayer–Vietoris_sequence wikiPageWikiLink Homotopy.
- Mayer–Vietoris_sequence wikiPageWikiLink Homotopy_equivalent.
- Mayer–Vietoris_sequence wikiPageWikiLink Homotopy_group.
- Mayer–Vietoris_sequence wikiPageWikiLink Homotopy_groups_of_spheres.
- Mayer–Vietoris_sequence wikiPageWikiLink Image_(mathematics).
- Mayer–Vietoris_sequence wikiPageWikiLink Inclusion_map.
- Mayer–Vietoris_sequence wikiPageWikiLink Injective_function.
- Mayer–Vietoris_sequence wikiPageWikiLink Interior_(topology).
- Mayer–Vietoris_sequence wikiPageWikiLink Intersection_(set_theory).
- Mayer–Vietoris_sequence wikiPageWikiLink Invariant_theory.
- Mayer–Vietoris_sequence wikiPageWikiLink Kernel_(algebra).
- Mayer–Vietoris_sequence wikiPageWikiLink Klein_bottle.
- Mayer–Vietoris_sequence wikiPageWikiLink Kronecker_delta.
- Mayer–Vietoris_sequence wikiPageWikiLink Lecture_Notes_in_Mathematics.
- Mayer–Vietoris_sequence wikiPageWikiLink Leopold_Vietoris.
- Mayer–Vietoris_sequence wikiPageWikiLink Linear_algebra.
- Mayer–Vietoris_sequence wikiPageWikiLink List_of_cohomology_theories.
- Mayer–Vietoris_sequence wikiPageWikiLink Long_exact_sequence.
- Mayer–Vietoris_sequence wikiPageWikiLink Long_exact_sequence_in_homology.
- Mayer–Vietoris_sequence wikiPageWikiLink Mathematical_induction.
- Mayer–Vietoris_sequence wikiPageWikiLink Mathematics.
- Mayer–Vietoris_sequence wikiPageWikiLink Mayer–Vietoris_sequence.
- Mayer–Vietoris_sequence wikiPageWikiLink Mayer–Vietoris_spectral_sequence.
- Mayer–Vietoris_sequence wikiPageWikiLink Monatshefte_für_Mathematik.
- Mayer–Vietoris_sequence wikiPageWikiLink Morphism.
- Mayer–Vietoris_sequence wikiPageWikiLink Möbius_strip.
- Mayer–Vietoris_sequence wikiPageWikiLink N-sphere.
- Mayer–Vietoris_sequence wikiPageWikiLink Natural_(category_theory).
- Mayer–Vietoris_sequence wikiPageWikiLink Natural_transformation.
- Mayer–Vietoris_sequence wikiPageWikiLink Neighbourhood_(mathematics).
- Mayer–Vietoris_sequence wikiPageWikiLink Non-empty.
- Mayer–Vietoris_sequence wikiPageWikiLink Norman_Steenrod.
- Mayer–Vietoris_sequence wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Mayer–Vietoris_sequence wikiPageWikiLink Object_(category_theory).
- Mayer–Vietoris_sequence wikiPageWikiLink Open_cover.
- Mayer–Vietoris_sequence wikiPageWikiLink Oxford_University_Press.
- Mayer–Vietoris_sequence wikiPageWikiLink Partition_of_unity.
- Mayer–Vietoris_sequence wikiPageWikiLink Path-connected.
- Mayer–Vietoris_sequence wikiPageWikiLink Princeton_University_Press.