Wikipedia:WikiProject Mathematics/PlanetMath Exchange/55-XX Algebraic topology
This page provides a list of all articles available at PlanetMath in the following topic:
- 55-XX Algebraic topology.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
edit- PM: invariance of dimension, id=4390 -- WP: invariance of dimension -- Status: A
- PM: universal coefficient theorem, id=4041 -- WP: universal coefficient theorem -- Status: NM
- PM: proof of invariance of dimension, id=7954new! -- WP guess: proof of invariance of dimension -- Status:
- PM: Thom class, id=7621new! -- WP guess: Thom class -- Status:
- PM: Thom isomorphism theorem, id=7622new! -- WP guess: Thom isomorphism theorem -- Status:
55M05 Duality
edit- PM: Poincaré duality, id=3652 -- WP: Poincare duality -- Status: A
55M20 Fixed points and coincidences
edit- PM: Sperner's lemma, id=4436 -- WP: Sperner's lemma -- Status: NM
55M25 Degree, winding number
edit- PM: degree (map of spheres), id=3897 -- WP: Degree of a continuous mapping -- Status: NM
55M30 Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
edit- PM: Lusternik-Schnirelmann category, id=7893new! -- WP guess: Lusternik-Schnirelmann category -- Status:
- PM: round complexity, id=7918new! -- WP guess: round complexity -- Status:
55M99 Miscellaneous
edit- PM: genus of topological surface, id=3296 -- WP: genus of topological surface -- Status: NM
- PM: standard n-ball, id=9133new! -- WP guess: standard n-ball -- Status:
55Mxx Classical topics
edit55N05 Cech types
edit- PM: de Rham cohomology, id=5913 -- WP: de Rham cohomology -- Status:
- PM: example of de Rham cohomology, id=5922 -- WP: de Rham cohomology -- Status:
55N10 Singular theory
edit- PM: Betti number, id=4498 -- WP: Betti number -- Status: A
- PM: cellular homology, id=3725 -- WP: cellular homology -- Status: NM
- PM: homology, id=3720 -- WP: homology (mathematics) -- Status: NM
- PM: homology of \mathbb{RP}^3., id=4576 -- WP guess: homology of \mathbbRP^3. -- Status: N
- PM: long exact sequence (of homology groups), id=3723 -- WP: Long exact sequence -- Status:
- PM: Mayer-Vietoris sequence, id=3724 -- WP guess: Mayer-Vietoris sequence -- Status:
- PM: relative homology groups, id=3722 -- WP: relative homology groups -- Status: A
55N25 Homology with local coefficients, equivariant cohomology
edit- PM: group cohomology (topological definition), id=6085new! -- WP guess: group cohomology (topological definition) -- Status:
55N45 Products and intersections
edit- PM: cap product, id=8589new! -- WP guess: cap product -- Status:
- PM: cup product, id=7554new! -- WP guess: cup product -- Status:
55N99 Miscellaneous
edit- PM: suspension isomorphism, id=3993 -- WP guess: suspension isomorphism -- Status:
- PM: Euler characteristic, id=8311new! -- WP guess: Euler characteristic -- Status:
55Nxx Homology and cohomology theories
edit55P05 Homotopy extension properties, cofibrations
edit- PM: cofibration, id=1598 -- WP guess: cofibration -- Status:
- PM: homotopy extension property, id=1600 -- WP guess: homotopy extension property -- Status:
55P10 Homotopy equivalences
edit- PM: homotopy equivalence, id=1589 -- WP: homotopy equivalence -- Status: A
- PM: weak homotopy equivalence, id=3987 -- WP: weak homotopy equivalence -- Status: A
- PM: Whitehead theorem, id=3988 -- WP: Whitehead theorem -- Status: A
- PM: nullhomotopic map, id=4858new! -- WP guess: nullhomotopic map -- Status:
55P15 Classification of homotopy type
edit- PM: simply connected, id=911 -- WP: simply connected -- Status: A
55P20 Eilenberg-Mac Lane spaces
edit- PM: Eilenberg-Mac Lane space, id=3986 -- WP: Eilenberg-Mac Lane space -- Status: A
55P45 $$-spaces and duals
edit55P99 Miscellaneous
edit- PM: fundamental groupoid, id=3941 -- WP: fundamental groupoid -- Status: NC
- Jtwdog 21:06, 26 September 2005 (UTC)
- Changed from A to NC, as the PM article is currently deeper than the WP single-sentence defnintion. linas 14:54, 15 April 2007 (UTC)
55Pxx Homotopy theory
edit55Q05 Homotopy groups, general; sets of homotopy classes
edit- PM: deformation retract, id=4121 -- WP guess: deformation retract -- Status:
- PM: fundamental group, id=849 -- WP: fundamental group -- Status: A
- PM: homotopy of maps, id=1584 -- WP guess: homotopy of maps -- Status:
- PM: homotopy of paths, id=1576 -- WP guess: homotopy of paths -- Status:
- PM: long exact sequence (locally trivial bundle), id=3726 -- WP guess: long exact sequence (locally trivial bundle) -- Status:
- PM: Van Kampen's theorem, id=3947 -- WP: Van Kampen's theorem -- Status: NM
- The PM article has commuting diagrams that should be copied over. linas 15:03, 15 April 2007 (UTC)
- PM: Van Kampen's theorem result, id=5576 -- WP: Van Kampen's theorem -- Status: NM
- Another nice box diagram to be copied over. linas 15:08, 15 April 2007 (UTC)
- PM: deformation retract is transitive, id=7683new! -- WP guess: deformation retract is transitive -- Status:
55Q52 Homotopy groups of special spaces
edit- PM: contractible, id=1594 -- WP guess: contractible -- Status:
55Qxx Homotopy groups
edit55R05 Fiber spaces
edit- PM: classification of covering spaces, id=4033 -- WP guess: classification of covering spaces -- Status:
- PM: covering space, id=910 -- WP guess: covering space -- Status:
- PM: deck transformation, id=4010 -- WP guess: deck transformation -- Status:
- PM: lifting of maps, id=3961 -- WP guess: lifting of maps -- Status:
- PM: lifting theorem, id=3963 -- WP guess: lifting theorem -- Status:
- PM: regular covering, id=4027 -- WP guess: regular covering -- Status:
55R10 Fiber bundles
edit- PM: associated bundle construction, id=4009 -- WP guess: associated bundle construction -- Status:
- PM: bundle map, id=3557 -- WP guess: bundle map -- Status:
- PM: fiber bundle, id=3551 -- WP guess: fiber bundle -- Status:
- PM: locally trivial bundle, id=3727 -- WP guess: locally trivial bundle -- Status:
- PM: principal bundle, id=3555 -- WP guess: principal bundle -- Status:
- PM: pullback bundle, id=3775 -- WP guess: pullback bundle -- Status:
- PM: reduction of structure group, id=3995 -- WP guess: reduction of structure group -- Status:
- PM: section of a fiber bundle, id=4008 -- WP guess: section of a fiber bundle -- Status:
- PM: some examples of universal bundles, id=3663 -- WP guess: some examples of universal bundles -- Status:
- PM: universal bundle, id=3556 -- WP guess: universal bundle -- Status:
- PM: 4 surface bundles, id=8070new! -- WP guess: 4 surface bundles -- Status:
- PM: surface bundle over the circle, id=7657new! -- WP guess: surface bundle over the circle -- Status:
55R15 Classification
edit55R25 Sphere bundles and vector bundles
edit- PM: Hopf bundle, id=3848 -- WP guess: Hopf bundle -- Status:
- PM: vector bundle, id=3554 -- WP guess: vector bundle -- Status:
- PM: gauge group, id=9331new! -- WP guess: gauge group -- Status:
- PM: sheaf of sections, id=7734new! -- WP guess: sheaf of sections -- Status:
- PM: Thom space, id=7620new! -- WP guess: Thom space -- Status:
55R65 Generalizations of fiber spaces and bundles
edit- PM: homotopy lifting property, id=7561new! -- WP guess: homotopy lifting property -- Status:
55Rxx Fiber spaces and bundles
edit55S37 Classification of mappings
edit55Sxx Operations and obstructions
edit55T05 General
edit55Txx Spectral sequences
edit55U05 Abstract complexes
edit- PM: barycentric subdivision, id=9080new! -- WP guess: barycentric subdivision -- Status:
55U10 Simplicial sets and complexes
edit- PM: simplicial complex, id=2828 -- WP guess: simplicial complex -- Status:
- PM: simplicial approximation, id=9166new! -- WP guess: simplicial approximation -- Status:
- PM: simplicial approximation theorem, id=9168new! -- WP guess: simplicial approximation theorem -- Status:
- PM: simplicial mapping, id=9167new! -- WP guess: simplicial mapping -- Status: