About: Surgery exact sequence

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Surgery exact sequence Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FSurgery_exact_sequence

In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension . The surgery structure set of a compact -dimensional manifold is a pointed set which classifies -dimensional manifolds within the homotopy type of .

Attributes	Values
rdfs:label	Surgery exact sequence (en)
rdfs:comment	In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension . The surgery structure set of a compact -dimensional manifold is a pointed set which classifies -dimensional manifolds within the homotopy type of . (en)
dcterms:subject	Surgery theory
Wikipage page ID	21298455 (xsd:integer)
Wikipage revision ID	1016301885 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Projective space C.T.C. Wall Non-simply-connected Dennis Sullivan Algebraic topology L-theory Surgery obstruction Quadratic forms Surgery theory Generalized Poincaré conjecture Frank Quinn (mathematician) Fundamental group William Browder (mathematician) H-cobordism American Mathematical Society Abelian group Surgery theory Cohomology Homotopy sphere Whitehead torsion Aspherical space Assembly map Manifold Borel conjecture Group ring Category (mathematics) Chain complex Sergei Novikov (mathematician) Topological manifold Pointed set Characteristic classes Surgery structure set S-cobordism Normal invariants Springer-Verlag Farrell-Jones Conjecture Simply-connected Pontrjagin-Thom construction
Link from a Wikipage to an external page	http://www.maths.ed.ac.uk/~aar/books/topman.pdf http://www.maths.ed.ac.uk/~aar/books/surgery.pdf http://131.220.77.52/lueck/data/ictp.pdf
sameAs	Surgery exact sequence Surgery exact sequence Surgery exact sequence
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Main dbt:Reflist dbt:Short_description
has abstract	In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension . The surgery structure set of a compact -dimensional manifold is a pointed set which classifies -dimensional manifolds within the homotopy type of . The basic idea is that in order to calculate it is enough to understand the other terms in the sequence, which are usually easier to determine. These are on one hand the normal invariants which form generalized cohomology groups, and hence one can use standard tools of algebraic topology to calculate them at least in principle. On the other hand, there are the L-groups which are defined algebraically in terms of quadratic forms or in terms of chain complexes with quadratic structure. A great deal is known about these groups. Another part of the sequence are the surgery obstruction maps from normal invariants to the L-groups. For these maps there are certain characteristic classes formulas, which enable to calculate them in some cases. Knowledge of these three components, that means: the normal maps, the L-groups and the surgery obstruction maps is enough to determine the structure set (at least up to extension problems). In practice one has to proceed case by case, for each manifold it is a unique task to determine the surgery exact sequence, see some examples below. Also note that there are versions of the surgery exact sequence depending on the category of manifolds we work with: smooth (DIFF), PL, or topological manifolds and whether we take Whitehead torsion into account or not (decorations or ). The original 1962 work of Browder and Novikov on the existence and uniqueness of manifolds within a simply-connected homotopy type was reformulated by Sullivan in 1966 as a surgery exact sequence.In 1970 Wall developed non-simply-connected surgery theory and the surgery exact sequence for manifolds with arbitrary fundamental group. (en)
prov:wasDerivedFrom	wikipedia-en:Surgery_exact_sequence?oldid=1016301885&ns=0
page length (characters) of wiki page	16799 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Surgery_exact_sequence
is Link from a Wikipage to another Wikipage of	Witt group William Browder (mathematician) Exotic sphere Surgery theory Assembly map Surgery structure set
is foaf:primaryTopic of	wikipedia-en:Surgery_exact_sequence

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software