Wikipedia:WikiProject Mathematics/PlanetMath Exchange/55-XX Algebraic topology

55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

 * PM: invariance of dimension, id=4390 -- WP: invariance of dimension -- Status: A
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)


 * PM: universal coefficient theorem, id=4041 -- WP: universal coefficient theorem -- Status: NM
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)


 * 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

 * PM: PoincarÃ© duality, id=3652 -- WP: Poincare duality -- Status: A
 * Jtwdog 21:06, 26 September 2005 (UTC)

55M20 Fixed points and coincidences

 * PM: Sperner's lemma, id=4436 -- WP: Sperner's lemma -- Status: NM
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)

55M25 Degree, winding number

 * PM: degree (map of spheres), id=3897 -- WP: Degree of a continuous mapping -- Status: NM
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)

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:

55M99 Miscellaneous

 * PM: genus of topological surface, id=3296 -- WP: genus of topological surface -- Status: NM
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)


 * PM: standard n-ball, id=9133new! -- WP guess: standard n-ball -- Status:

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:

55N10 Singular theory

 * PM: Betti number, id=4498 -- WP: Betti number -- Status: A
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)


 * PM: cellular homology, id=3725 -- WP: cellular homology -- Status: NM
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)


 * PM: homology, id=3720 -- WP: homology (mathematics) -- Status: NM
 * Tom pw (talk) 14:26, 21 March 2007 (UTC)


 * PM: homology of \mathbb{RP}^3., id=4576 -- WP guess: homology of \mathbbRP^3. -- Status: N
 * Tom pw (talk) 15:12, 23 March 2007 (UTC)


 * 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)

55N25 Homology with local coefficients, equivariant cohomology

 * PM: group cohomology (topological definition), id=6085new! -- WP guess: group cohomology (topological definition) -- Status:

55N45 Products and intersections

 * PM: cap product, id=8589new! -- WP guess: cap product -- Status:


 * PM: cup product, id=7554new! -- WP guess: cup product -- Status:

55N99 Miscellaneous

 * PM: suspension isomorphism, id=3993 -- WP guess: suspension isomorphism -- Status:


 * PM: Euler characteristic, id=8311new! -- WP guess: Euler  characteristic -- Status:

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:

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:

55P15 Classification of homotopy type

 * PM: simply connected, id=911 -- WP: simply connected -- Status: A
 * Jtwdog 20:04, 26 September 2005 (UTC)

55P20 Eilenberg-Mac Lane spaces

 * PM: Eilenberg-Mac Lane space, id=3986 -- WP: Eilenberg-Mac Lane space -- Status: A
 * Jtwdog 21:06, 26 September 2005 (UTC)

55P45 $$-spaces and duals

 * PM: H-space, id=8427new! -- WP guess: H-space -- Status:

55P99 Miscellaneous

 * 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)

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
 * 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

 * PM: contractible, id=1594 -- WP guess: contractible -- Status:

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:


 * PM: monodromy, id=4000 -- WP: monodromy -- Status: A
 * linas 04:45, 20 December 2006 (UTC)


 * PM: regular covering, id=4027 -- WP guess: regular covering -- Status:

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:

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:

55R65 Generalizations of fiber spaces and bundles

 * PM: fibration, id=7560new! -- WP guess: fibration -- Status:


 * PM: homotopy lifting property, id=7561new! -- WP guess: homotopy lifting property -- Status:

55S37 Classification of mappings

 * PM: wild, id=9135new! -- WP guess: wild -- Status:

55U05 Abstract complexes

 * PM: barycentric subdivision, id=9080new! -- WP guess: barycentric subdivision -- Status:

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: