Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A Künneth formula in topological homology and its applications to the simplicial cohomology of $ℓ¹(ℤ₊^{k})$

100%

Gourdeau F., Lykova Z., White M.

Studia Mathematica

2005

tom 166

nr 1

29-54

We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex 𝓧 of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(𝓧') ≅ Hₙ(𝓧)', where Hₙ(𝓧)' is the dual space of the homology group of 𝓧 and Hⁿ(𝓧') is the cohomology group of the dual complex 𝓧'. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly the simplicial cohomology groups $ℋⁿ(ℓ¹(ℤ₊^{k}),ℓ¹(ℤ₊^{k})')$ and homology groups $ℋₙ(ℓ¹(ℤ₊^{k}),ℓ¹(ℤ₊^{k}))$ of the semigroup algebra $ℓ¹(ℤ₊^{k})$.

Ograniczanie wyników

1 Studia Mathematica

1 Gourdeau F.

1 Lykova Z.

1 White M.

1 2005

Wyniki wyszukiwania

A Künneth formula in topological homology and its applications to the simplicial cohomology of $ℓ¹(ℤ₊^{k})$