About: Homotopy groups of spheres

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

About: Homotopy groups of spheres Goto Sponge NotDistinct Permalink

An Entity of Type : yago:State100024720, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FHomotopy_groups_of_spheres

In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry. Unlike homology groups, which are also topological invariants, the homotopy groups are surprisingly complex and difficult to compute. The problem of determining πi(Sn) falls into three regimes, depending on whether i is less than, equal to, or greater than n:

Attributes	Values
rdf:type	yago:WikicatSpheres yago:Abstraction100002137 yago:Attribute100024264 yago:Environment113934596 yago:Situation113927383 yago:Sphere114514039 yago:State100024720
rdfs:label	Grupos de homotopía de esferas (es) Homotopy groups of spheres (en) Groupes d'homotopie des sphères (fr) Гомотопические группы сфер (ru)
rdfs:comment	En mathématiques, et plus spécifiquement en topologie algébrique, les groupes d'homotopie des sphères sont des invariants qui décrivent, en termes algébriques, comment des sphères de dimensions et égales ou différentes peuvent s'enrouler l'une sur l'autre. La notion, définie au départ pour des sphères de dimension 1 (cercles) et de dimension 2, se généralise à des sphères de toutes dimensions (les -sphères). (fr) En el campo matemático de topología algebraica, los grupos de homotopía de esferas describen cómo esferas de variadas dimensiones pueden envolverse unas a otras. Son ejemplos de invariantes topológicas, las cuales reflejan, en términos algebraicos, la estructura de esferas vistas como espacios topológicos, olvidando detalles geométricos precisos. A diferencia de los grupos de homología, los cuales son también invariantes topológicas, los grupos de homotopía son sorprendentemente complejos y difíciles de calcular. * Datos: Q3118090 (es) In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry. Unlike homology groups, which are also topological invariants, the homotopy groups are surprisingly complex and difficult to compute. The problem of determining πi(Sn) falls into three regimes, depending on whether i is less than, equal to, or greater than n: (en) Гомотопические группы сфер — один из основных объектов изучения теории гомотопий, области алгебраической топологии. Гомотопические группы сфер классифицируют отображения между многомерными сферами с точностью до непрерывной деформации. Гомотопические группы сфер являются дискретными алгебраическими объектами, а именно конечнопорождёнными абелевыми группами. Несмотря на то, что классификация конечнопорождённых абелевых групп очень проста, точная структура гомотопических групп сфер до конца неизвестна. (ru)
foaf:depiction
dcterms:subject	Spheres Homotopy theory
Wikipage page ID	1104697 (xsd:integer)
Wikipage revision ID	1114224136 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Camille Jordan Cartesian product Princeton University Press Quaternion Kervaire invariant problem Barratt–Priddy theorem Bernoulli number Borromean rings Braid group Algebraic topology Annals of Mathematics Hopf fibration José Adem Pavel Alexandrov René Thom Residue theorem Curve EHP spectral sequence J-homomorphism Line segment Topological invariant Trivial group Complex analysis Complex number Continuous map Critical point (mathematics) Analysis Situs (paper) Mathematics Geometric group theory Normal bundle Notices of the American Mathematical Society Origin (mathematics) Smooth structure Circle Classifying space Elsevier Frank Adams Fundamental theorem of algebra Generating set of a group Geometry George W. Whitehead Boundary (topology) Braid Modular arithmetic N-sphere Congruence relation Contractible space Critical value Equator Equivalence class Nilpotent Lev Pontryagin Short exact sequence Singularity theory Slash (punctuation) Complex cobordism Component (group theory) Freudenthal suspension theorem Fundamental group Hopf invariant Kervaire invariant Mathematische Annalen Rubber band Path connected Subgroup Suspension (topology) May spectral sequence Ball (mathematics) Acta Mathematica Adams spectral sequence Topology H-cobordism

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 (61 GB total memory, 42 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software