Stable cohomology operation - Revision history

Vipul: 3 revisions

2008-05-11T19:59:01Z

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Vipul at 22:16, 13 December 2007

2007-12-13T22:16:15Z

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	{{source\|[[sor:C/c023150.htm\|Springer Online Reference Works]]}}		{{source\|[[sor:C/c023150.htm\|Springer Online Reference Works]]}}

			{{particularcases\|[[:Category:Stable cohomology operations]]}}

	==Definition==		==Definition==

Vipul at 22:10, 13 December 2007

2007-12-13T22:10:19Z

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	{{source\|[[sor:C/c023150\|Springer Online Reference Works]]}}		{{source\|[[sor:C/c023150.htm\|Springer Online Reference Works]]}}

	==Definition==		==Definition==

	A '''stable cohomology operation''' of ''type'' <math>(\pi,G)</math> and of ''degree'' <math>k</math> is defined as		A '''stable cohomology operation''' of ''type'' <math>(\pi,G)</math> and of ''degree'' <math>k</math> is defined as a set <math>\{ \theta_n \}_{-\infty}^{\infty}</math> of [[cohomology operation]]s <math>\theta_n</math> of type <math>(n,n+k,\pi,G)</math> such that <math>\theta_{n-1}</math> is the [[cohomology suspension]] of <math>\theta_n</math>.

			For a stable cohomology operation, all its constituent cohomology operations are group homomorphisms (this is not true for [[cohomology operation]]s in isolation).

Vipul at 22:06, 13 December 2007

2007-12-13T22:06:50Z

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{{source|[[sor:C/c023150|Springer Online Reference Works]]}}

==Definition==

A '''stable cohomology operation''' of ''type'' <math>(\pi,G)</math> and of ''degree'' <math>k</math> is defined as