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- Manifold_decomposition abstract "In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form M.Manifold decomposition works in two directions: one can start with the smaller pieces and build up a manifold, or start with a large manifold and decompose it. The latter has proven a very useful way to study manifolds: without tools like decomposition, it is sometimes very hard to understand a manifold. In particular, it has been useful in attempts to classify 3-manifolds and also in proving the higher-dimensional Poincaré conjecture.The table below is a summary of the various manifold-decomposition techniques. The column labeled "M" indicates what kind of manifold can be decomposed; the column labeled "How it is decomposed" indicates how, starting with a manifold, one can decompose it into smaller pieces; the column labeled "The pieces" indicates what the pieces can be; and the column labeled "How they are combined" indicates how the smaller pieces are combined to make the large manifold.".
- Manifold_decomposition wikiPageID "1227329".
- Manifold_decomposition wikiPageLength "4008".
- Manifold_decomposition wikiPageOutDegree "57".
- Manifold_decomposition wikiPageRevisionID "603813102".
- Manifold_decomposition wikiPageWikiLink 3-manifold.
- Manifold_decomposition wikiPageWikiLink Adjunction_space.
- Manifold_decomposition wikiPageWikiLink Atoroidal.
- Manifold_decomposition wikiPageWikiLink Ball.
- Manifold_decomposition wikiPageWikiLink Ball_(mathematics).
- Manifold_decomposition wikiPageWikiLink Category:Geometric_topology.
- Manifold_decomposition wikiPageWikiLink Closed_manifold.
- Manifold_decomposition wikiPageWikiLink Compact_space.
- Manifold_decomposition wikiPageWikiLink Connected_sum.
- Manifold_decomposition wikiPageWikiLink Critical_point_(mathematics).
- Manifold_decomposition wikiPageWikiLink Differentiable_manifold.
- Manifold_decomposition wikiPageWikiLink Edwin_E._Moise.
- Manifold_decomposition wikiPageWikiLink Haken_hierarchy.
- Manifold_decomposition wikiPageWikiLink Haken_manifold.
- Manifold_decomposition wikiPageWikiLink Handle_(mathematics).
- Manifold_decomposition wikiPageWikiLink Handle_decomposition.
- Manifold_decomposition wikiPageWikiLink Handlebody.
- Manifold_decomposition wikiPageWikiLink Heegaard_splitting.
- Manifold_decomposition wikiPageWikiLink Irreducibility_(mathematics).
- Manifold_decomposition wikiPageWikiLink Irreducible_(mathematics).
- Manifold_decomposition wikiPageWikiLink JSJ_decomposition.
- Manifold_decomposition wikiPageWikiLink Link_(knot_theory).
- Manifold_decomposition wikiPageWikiLink Manifold.
- Manifold_decomposition wikiPageWikiLink Mathematics.
- Manifold_decomposition wikiPageWikiLink Morse_function.
- Manifold_decomposition wikiPageWikiLink Morse_theory.
- Manifold_decomposition wikiPageWikiLink Open_book_decomposition.
- Manifold_decomposition wikiPageWikiLink Orientability.
- Manifold_decomposition wikiPageWikiLink Orientable.
- Manifold_decomposition wikiPageWikiLink Poincaré_conjecture.
- Manifold_decomposition wikiPageWikiLink Prime_decomposition_(3-manifold).
- Manifold_decomposition wikiPageWikiLink Prime_manifold.
- Manifold_decomposition wikiPageWikiLink Seifert-fibered_space.
- Manifold_decomposition wikiPageWikiLink Seifert_fiber_space.
- Manifold_decomposition wikiPageWikiLink Simplex.
- Manifold_decomposition wikiPageWikiLink Smooth_manifold.
- Manifold_decomposition wikiPageWikiLink Sphere.
- Manifold_decomposition wikiPageWikiLink Surgery_theory.
- Manifold_decomposition wikiPageWikiLink Sutured_manifold.
- Manifold_decomposition wikiPageWikiLink Topology.
- Manifold_decomposition wikiPageWikiLink Torus.
- Manifold_decomposition wikiPageWikiLink Triangulation_(topology).
- Manifold_decomposition wikiPageWikiLink Trigenus.
- Manifold_decomposition wikiPageWikiLinkText "Manifold decomposition".
- Manifold_decomposition wikiPageWikiLinkText "decomposition".
- Manifold_decomposition wikiPageWikiLinkText "manifold decomposition".
- Manifold_decomposition hasPhotoCollection Manifold_decomposition.
- Manifold_decomposition wikiPageUsesTemplate Template:Expand_list.
- Manifold_decomposition wikiPageUsesTemplate Template:Unreferenced.
- Manifold_decomposition subject Category:Geometric_topology.
- Manifold_decomposition type Article.
- Manifold_decomposition type List.
- Manifold_decomposition type Article.
- Manifold_decomposition type List.
- Manifold_decomposition comment "In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form M.Manifold decomposition works in two directions: one can start with the smaller pieces and build up a manifold, or start with a large manifold and decompose it.".
- Manifold_decomposition label "Manifold decomposition".
- Manifold_decomposition sameAs m.04k4xh.
- Manifold_decomposition sameAs Q6749571.
- Manifold_decomposition sameAs Q6749571.
- Manifold_decomposition wasDerivedFrom Manifold_decomposition?oldid=603813102.
- Manifold_decomposition isPrimaryTopicOf Manifold_decomposition.