A
–local
compact group is an algebraic object modelled on the homotopy theory associated with
–completed
classifying spaces of compact Lie groups and
–compact groups.
In particular
–local
compact groups give a unified framework in which one may study
–completed classifying
spaces from an algebraic and homotopy theoretic point of view. Like connected compact Lie groups
and
–compact
groups,
–local
compact groups admit unstable Adams operations: self equivalences that are
characterised by their cohomological effect. Unstable Adams operations on
–local
compact groups were constructed in a previous paper by F Junod, R Levi, and
A Libman. In the present paper we study groups of unstable operations from a
geometric and algebraic point of view. We give a precise description of the
relationship between algebraic and geometric operations, and show that under
some conditions, unstable Adams operations are determined by their degree.
We also examine a particularly well behaved subgroup of unstable Adams
operations.
