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Homotopy 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.

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Overview

Background

Low-dimensional examples

History

General theory

Computational methods

Applications

Table of homotopy groups

General algebraic topology references

Historical papers

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Homotopy groups of spheres

Nodes190
Edges189
Triples149
Avg. degree1.99
Density0.010526
Components1

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Homotopy groups of spheres

Top relations

related to history · 29
Homotopy groups of spheres → An, Analysis, Camille Jordan, Daniel Isaksen, Eduard, Frank Adams, George, Guozhen Wang, Hans Freudenthal's, Heinz Hopf, Henri Poincaré, Higher, Hiroshi Toda, His, In, Jean-Pierre Serre, José Adem, Mark Mahowald, Others, Pavel Sergeyevich Alexandrov
has method · 25
Homotopy groups of spheres → Adams, At, Brown, CartanandSerre, Consequently, E2, Eilenberg, Ext, He, Hurewicz, If, In, MacLane, May, Novikov, Peterson, Serre, Steenrod, The, The EHP
has application · 16
Homotopy groups of spheres → Brouwer, For, K-theory, Kervaire, More, Priddy, Rokhlin's, S1, Sn, Stable, Such, The, The Barratt, The Kervaire, This, Vladimir Rokhlin
related to Framed cobordism · 16
Homotopy groups of spheres → Every, For, Homotopy, Hopf, In, Lev Pontryagin, Mk, Pontrjagin, René Thom, S1, S2, S3, Serre, Sn, The, Until
related to External links · 14
Homotopy groups of spheres → Allen, April, Baez, Connor, John, MacTutor History, Marie Ennemond Camille Jordan, Mathematics, O'Connor, PDF, Robertson, Stable, This, Topology
related to The J-homomorphism · 10
Homotopy groups of spheres → An, B2m, B2m/4m, Bernoulli, Bott, In, J-homomorphism, Sn, SO, This
related to Finiteness and torsion · 9
Homotopy groups of spheres → Furthermore, If, In, Jean-Pierre Serre, S2n, Serre, Sn, The, This
related to Table · 8
Homotopy groups of spheres → Extended, In, S1, The, Z2, Z24, Z3, Zn
related to π2(S1) = 0 · 7
Homotopy groups of spheres → All, Hence, In, S1, S2, This, Unfortunately
related to Stable and unstable groups · 4
Homotopy groups of spheres → For, Hans Freudenthal, Sn, The

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Important terminology

homotopy groups group sn spheres stable sphere map πn one topology s1 algebraic space first maps s2 theorem πi hopf

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Homotopy groups of spheresis asupercommutative graded ring0.90text
Homotopy groups of sphereshas applicationThe0.60section
Homotopy groups of sphereshas applicationS10.60section
Homotopy groups of sphereshas applicationSn0.60section
Homotopy groups of sphereshas applicationBrouwer0.60section
Homotopy groups of sphereshas applicationSuch0.60section
Homotopy groups of sphereshas applicationVladimir Rokhlin0.60section
Homotopy groups of sphereshas applicationRokhlin's0.60section
Homotopy groups of sphereshas applicationStable0.60section
Homotopy groups of sphereshas applicationMore0.60section
Homotopy groups of sphereshas applicationThe Kervaire0.60section
Homotopy groups of sphereshas applicationKervaire0.60section

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