Conductivity near the percolation threshold
In mathematics, the inflation-restriction exact sequence is an exact sequence occurring in group cohomology and is a special case of the five-term exact sequence arising from the study of spectral sequences.
Specifically, let G be a group, N a normal subgroup, and A an abelian group which is equipped with an action of G, i.e., a homomorphism from G to the automorphism group of A. The quotient group G/N acts on AN = { a A : na = a for all n N}. Then the inflation-restriction exact sequence is:
- 0 → H 1(G/N, AN) → H 1(G, A) → H 1(N, A)G/N → H 2(G/N, AN) →H 2(G, A)
In this sequence, there are maps
- inflation H 1(G/N, AN) → H 1(G, A)
- restriction H 1(G, A) → H 1(N, A)G/N
- transgression H 1(N, A)G/N → H 2(G/N, AN)
- inflation H 2(G/N, AN) →H 2(G, A)
The inflation and restriction are defined for general n:
- inflation Hn(G/N, AN) → Hn(G, A)
- restriction Hn(G, A) → Hn(N, A)G/N
The transgression is defined for general n
- transgression Hn(N, A)G/N → Hn+1(G/N, AN)
only if Hi(N, A)G/N = 0 for i ≤ n-1.[1]
The sequence for general n may be deduced from the case n=1 by dimension-shifting or from the Lyndon–Hochschild–Serre spectral sequence.[2]
References
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My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534