Wikipedia:WikiProject Mathematics/PlanetMath Exchange/55-XX Algebraic topology
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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.
[edit] 55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 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:
[edit] 55M05 Duality
- PM: Poincaré duality, id=3652 -- WP: Poincare duality -- Status: A
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- Jtwdog 21:06, 26 September 2005 (UTC)
[edit] 55M20 Fixed points and coincidences
- PM: Sperner's lemma, id=4436 -- WP: Sperner's lemma -- Status: NM
[edit] 55M25 Degree, winding number
- PM: degree (map of spheres), id=3897 -- WP: Degree of a continuous mapping -- Status: NM
[edit] 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
- PM: Lusternik-Schnirelmann category, id=7893new! -- WP guess: Lusternik-Schnirelmann category -- Status:
- PM: round complexity, id=7918new! -- WP guess: round complexity -- Status:
- PM: t-cat, id=7919new! -- WP guess: t-cat -- Status:
[edit] 55M99 Miscellaneous
- 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:
[edit] 55Mxx Classical topics
[edit] 55N05 Cech types
- PM: de Rham cohomology, id=5913 -- WP: de Rham cohomology -- Status:
- PM: example of de Rham cohomology, id=5922 -- WP: de Rham cohomology -- Status:
[edit] 55N10 Singular theory
- 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
-
- linas 14:37, 18 April 2007 (UTC)
[edit] 55N25 Homology with local coefficients, equivariant cohomology
- PM: group cohomology (topological definition), id=6085new! -- WP guess: group cohomology (topological definition) -- Status:
[edit] 55N45 Products and intersections
- PM: cap product, id=8589new! -- WP guess: cap product -- Status:
- PM: cup product, id=7554new! -- WP guess: cup product -- Status:
[edit] 55N99 Miscellaneous
- PM: suspension isomorphism, id=3993 -- WP guess: suspension isomorphism -- Status:
- PM: Euler characteristic, id=8311new! -- WP guess: Euler characteristic -- Status:
[edit] 55Nxx Homology and cohomology theories
[edit] 55P05 Homotopy extension properties, cofibrations
- PM: cofibration, id=1598 -- WP guess: cofibration -- Status:
- PM: homotopy extension property, id=1600 -- WP guess: homotopy extension property -- Status:
[edit] 55P10 Homotopy equivalences
- PM: homotopy equivalence, id=1589 -- WP: homotopy equivalence -- Status: A
-
- Jtwdog 21:06, 26 September 2005 (UTC)
- PM: weak homotopy equivalence, id=3987 -- WP: weak homotopy equivalence -- Status: A
-
- Jtwdog 21:06, 26 September 2005 (UTC)
- PM: Whitehead theorem, id=3988 -- WP: Whitehead theorem -- Status: A
-
- Jtwdog 21:06, 26 September 2005 (UTC)
- PM: nullhomotopic map, id=4858new! -- WP guess: nullhomotopic map -- Status:
[edit] 55P15 Classification of homotopy type
- PM: simply connected, id=911 -- WP: simply connected -- Status: A
-
- Jtwdog 20:04, 26 September 2005 (UTC)
[edit] 55P20 Eilenberg-Mac Lane spaces
- PM: Eilenberg-Mac Lane space, id=3986 -- WP: Eilenberg-Mac Lane space -- Status: A
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- Jtwdog 21:06, 26 September 2005 (UTC)
[edit] 55P45 $$-spaces and duals
[edit] 55P99 Miscellaneous
- PM: fundamental groupoid, id=3941 -- WP: fundamental groupoid -- Status: NC
[edit] 55Pxx Homotopy theory
[edit] 55Q05 Homotopy groups, general; sets of homotopy classes
- PM: deformation retract, id=4121 -- WP guess: deformation retract -- Status:
- PM: fundamental group, id=849 -- WP: fundamental group -- Status: A
-
- linas 14:59, 15 April 2007 (UTC)
- 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
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- 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:
[edit] 55Q52 Homotopy groups of special spaces
- PM: contractible, id=1594 -- WP guess: contractible -- Status:
[edit] 55Qxx Homotopy groups
[edit] 55R05 Fiber spaces
- 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:
-
- linas 04:45, 20 December 2006 (UTC)
- PM: regular covering, id=4027 -- WP guess: regular covering -- Status:
[edit] 55R10 Fiber bundles
- 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: fibre map, id=6087new! -- WP guess: fibre map -- Status:
- PM: surface bundle over the circle, id=7657new! -- WP guess: surface bundle over the circle -- Status:
[edit] 55R15 Classification
[edit] 55R25 Sphere bundles and vector bundles
- 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:
[edit] 55R65 Generalizations of fiber spaces and bundles
- PM: homotopy lifting property, id=7561new! -- WP guess: homotopy lifting property -- Status:
[edit] 55Rxx Fiber spaces and bundles
[edit] 55S37 Classification of mappings
[edit] 55Sxx Operations and obstructions
[edit] 55T05 General
[edit] 55Txx Spectral sequences
[edit] 55U05 Abstract complexes
- PM: barycentric subdivision, id=9080new! -- WP guess: barycentric subdivision -- Status:
[edit] 55U10 Simplicial sets and complexes
- 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: