Relations in the Homotopy of
Simplicial Abelian Hopf Algebras
by
James M. Turner
Submitted to the Department of Mathematics on May 10, 1994
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy in Mathematics
Abstract
In this paper, we analyze the structure possessed by the homotopy groups of
a simplicial abelian Hopfalgebra over the field F2. Specifically, we reviewthe
higher-order structure that the homotopy groups of a simplicial commutative
algebra and simplicial cocommutative coalgebra possess. We then demonstrate
how these structures interact under the added assumptions present in a Hopf
algebra.
Thesis Supervisor:Haynes R. Miller
Title: Professor of Mathematics