About: Normal invariant

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In mathematics, a normal map is a concept in geometric topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X (more geometrically a Poincaré space), a normal map on X endows the space, roughly speaking, with some of the homotopy-theoretic global structure of a closed manifold. In particular, X has a good candidate for a stable normal bundle and a Thom collapse map, which is equivalent to there being a map from a manifold M to X matching the fundamental classes and preserving normal bundle information. If the dimension of X is 5 there is then only the algebraic topology surgery obstruction due to C. T. C. Wall to X actually being homotopy equivalent to a closed manifold. Normal maps also apply to the study of the uniqueness of manif

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rdfs:label	Normal invariant (en)
rdfs:comment	In mathematics, a normal map is a concept in geometric topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X (more geometrically a Poincaré space), a normal map on X endows the space, roughly speaking, with some of the homotopy-theoretic global structure of a closed manifold. In particular, X has a good candidate for a stable normal bundle and a Thom collapse map, which is equivalent to there being a map from a manifold M to X matching the fundamental classes and preserving normal bundle information. If the dimension of X is 5 there is then only the algebraic topology surgery obstruction due to C. T. C. Wall to X actually being homotopy equivalent to a closed manifold. Normal maps also apply to the study of the uniqueness of manif (en)
dcterms:subject	Surgery theory
Wikipage page ID	21298614 (xsd:integer)
Wikipage revision ID	1032019697 (xsd:integer)
Link from a Wikipage to another Wikipage	René Thom Surgery obstruction Surgery theory Geometric topology Tangent bundle Homotopy equivalent Embedding C. T. C. Wall William Browder (mathematician) Poincaré duality American Mathematical Society Hassler Whitney Jim Stasheff Samuel Gitler Hammer Surgery theory Cobordism Thom Sergei Novikov (mathematician) Immersion (mathematics) Poincaré complex Poincaré space Stable normal bundle Springer-Verlag Whitehead's theorem Pontrjagin-Thom construction CW-complex
Link from a Wikipage to an external page	http://131.220.77.52/lueck/data/ictp.pdf http://www.maths.ed.ac.uk/~aar/books/index.htm
sameAs	Normal invariant Normal invariant Normal invariant
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:No_footnotes
has abstract	In mathematics, a normal map is a concept in geometric topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X (more geometrically a Poincaré space), a normal map on X endows the space, roughly speaking, with some of the homotopy-theoretic global structure of a closed manifold. In particular, X has a good candidate for a stable normal bundle and a Thom collapse map, which is equivalent to there being a map from a manifold M to X matching the fundamental classes and preserving normal bundle information. If the dimension of X is 5 there is then only the algebraic topology surgery obstruction due to C. T. C. Wall to X actually being homotopy equivalent to a closed manifold. Normal maps also apply to the study of the uniqueness of manifold structures within a homotopy type, which was pioneered by Sergei Novikov. The cobordism classes of normal maps on X are called normal invariants. Depending on the category of manifolds (differentiable, piecewise-linear, or topological), there are similarly defined, but inequivalent, concepts of normal maps and normal invariants. It is possible to perform surgery on normal maps, meaning surgery on the domain manifold, and preserving the map. Surgery on normal maps allows one to systematically kill elements in the relative homotopy groups by representing them as embeddings with trivial normal bundle. (en)
prov:wasDerivedFrom	wikipedia-en:Normal_invariant?oldid=1032019697&ns=0
page length (characters) of wiki page	13757 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Normal_invariant
is Link from a Wikipage to another Wikipage of	Dennis Sullivan Surgery obstruction Normal Normal map Obstruction theory William Browder (mathematician) Plumbing (mathematics) Poincaré space Normal invariants
is Wikipage redirect of	Normal invariants
is Wikipage disambiguates of	Normal
is foaf:primaryTopic of	wikipedia-en:Normal_invariant

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