Operations and Spectral Sequences I
James M. Turner
Department of Mathematics
University of Virginia
Charlottesville, VA 22903
Abstract: This is the first in a series of papers which examines a general
type a chain complex (over F_2) whose homology supports a well-defined action of
operations. We call such complexes Dold algebras, which include the
singular cochain complex of a space and the singular chain complex of an
infinite loop space, and we give conditions on filtrations of such objects
so that there is a compatible action of operations on the associated
spectral sequences. For applications, we recover W. Singer's result of the
action of Steenrod operations on the Serre spectral sequence and we extend
A. Bahri's action of Dyer-Lashof operations on the Eilenberg-Moore
spectral sequence.