Taylor towers of symmetric and exterior powers

• Autorzy: Brenda Johnson , Randy McCarthy
• Języki publikacji: EN

Abstrakty

EN

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 $D_{k}Λⁿ$.

Kategorie tematyczne

• 55U99: None of the above, but in this section
• 55P65: Homotopy functors
• 18G99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 201
• Numer: 3
• Strony: 197-216

Daty

wydano

2008

Twórcy

autor

Brenda Johnson

• Department of Mathematics, Union College, Schenectady, NY 12308, U.S.A.

autor

Randy McCarthy

• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, IL 61801, U.S.A.

Identyfikatory

DOI

10.4064/fm201-3-1