Wiki143: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

Tompw (talk) 14:26, 21 March 2007 (UTC)

• PM: universal coefficient theorem, id=4041 -- WP: universal coefficient theorem -- Status: NM

Tompw (talk) 14:26, 21 March 2007 (UTC)

• PM: proof of invariance of dimension, id=7954^new! -- WP guess: proof of invariance of dimension -- Status:

• PM: Thom class, id=7621^new! -- WP guess: Thom class -- Status:

• PM: Thom isomorphism theorem, id=7622^new! -- WP guess: Thom isomorphism theorem -- Status:

55M05 Duality

• PM: Poincaré 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

Tompw (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

Tompw (talk) 14:26, 21 March 2007 (UTC)

55M30 Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space

• PM: Lusternik-Schnirelmann category, id=7893^new! -- WP guess: Lusternik-Schnirelmann category -- Status:

• PM: round complexity, id=7918^new! -- WP guess: round complexity -- Status:

• PM: t-cat, id=7919^new! -- WP guess: t-cat -- Status:

55M99 Miscellaneous

• PM: genus of topological surface, id=3296 -- WP: genus of topological surface -- Status: NM

Tompw (talk) 14:26, 21 March 2007 (UTC)

• PM: standard n-ball, id=9133^new! -- 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

Tompw (talk) 14:26, 21 March 2007 (UTC)

• PM: cellular homology, id=3725 -- WP: cellular homology -- Status: NM

Tompw (talk) 14:26, 21 March 2007 (UTC)

• PM: homology, id=3720 -- WP: homology (mathematics) -- Status: NM

Tompw (talk) 14:26, 21 March 2007 (UTC)

• PM: homology of \mathbb{RP}^3., id=4576 -- WP guess: homology of \mathbbRP^3. -- Status: N

Tompw (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=6085^new! -- WP guess: group cohomology (topological definition) -- Status:

55N45 Products and intersections

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

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

55N99 Miscellaneous

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

• PM: Euler characteristic, id=8311^new! -- 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=4858^new! -- 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=8427^new! -- 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=7683^new! -- 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=8070^new! -- WP guess: 4 surface bundles -- Status:

• PM: fibre map, id=6087^new! -- WP guess: fibre map -- Status:

• PM: surface bundle over the circle, id=7657^new! -- 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=9331^new! -- WP guess: gauge group -- Status:

• PM: sheaf of sections, id=7734^new! -- WP guess: sheaf of sections -- Status:

• PM: Thom space, id=7620^new! -- WP guess: Thom space -- Status:

55R65 Generalizations of fiber spaces and bundles

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

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

55S37 Classification of mappings

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

55U05 Abstract complexes

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

55U10 Simplicial sets and complexes

• PM: simplicial complex, id=2828 -- WP guess: simplicial complex -- Status:

• PM: simplicial approximation, id=9166^new! -- WP guess: simplicial approximation -- Status:

• PM: simplicial approximation theorem, id=9168^new! -- WP guess: simplicial approximation theorem -- Status:

• PM: simplicial mapping, id=9167^new! -- WP guess: simplicial mapping -- Status: