CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:     Brenda Johnson, Union College 

Time:        Wednesday,  May 1, at 4:30pm, 

Place:       Harder Hall Rm. 203, Skidmore College  

Title:       Taylor towers and symmetric, exterior, and divided powers  
             

Abstract: 

Any functor $F$ of chain complexes over an abelian category
has associated to it a Taylor tower,
$$
\dots \rightarrow P_{n+1}F \rightarrow P_nF \rightarrow
P_{n-1}F \rightarrow \dots \rightarrow P_1F,
$$
in which each functor $P_nF$ is homologically degree $n$, i.e., its
$n+1$st cross effect in the sense of Eilenberg and Mac Lane is acyclic.
When $F(0)=0$, the first term in this tower is equivalent to the
stabilization of $F$ defined by Dold and  Puppe.  For the case in which
$F$ is the $n$th symmetric, exterior, or divided power functor, the
stabilization of $F$ has been studied extensively by Dold and Puppe,
Simson and Tyc, Bousfield, and others.  We show how their results
yield information about the higher terms in the Taylor towers of
these functors.
This is joint work with Randy McCarthy.


Refreshments at 4:15 in Harder Hall 203.