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Taylor towers of symmetric and exterior powers

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Johnson B., McCarthy R.

Fundamenta Mathematicae

2008

tom 201

nr 3

197-216

We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, $D_{k}Spⁿ$ and $D_{k}Λⁿ$, in terms of the first terms in the Taylor towers of $Sp^{t}$ and $Λ^{t}$ for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of $Sp^{t}$ and $Λ^{t}$. We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for $D_{k}Spⁿ$ and $D_{k}Λⁿ$.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Johnson B.

1 McCarthy R.

1 2008

Wyniki wyszukiwania

Taylor towers of symmetric and exterior powers