  A locally compact contraction group is a pair (G,f) where G is a locally
compact group and f an automorphism of G which is contractive in the sense that
the forward orbit under f of each g in G converges to the neutral element e, as
n tends to infinity. We show that every surjective, continuous, equivariant
homomorphism between locally compact contraction groups admits an equivariant
continuous global section. As a consequence, extensions of locally compact
contraction groups with abelian kernel can be described by continuous
equivariant cohomology. For each prime number p, we use 2-cocycles to construct
uncountably many pairwise non-isomorphic totally disconnected, locally compact
contraction groups (G,f) which are central extensions of the additive group of
the field of formal Laurent series over Z/pZ by itself. By contrast, there are
only countably many locally compact contraction groups (up to isomorphism)
which are torsion groups and abelian, as follows from a classification of the
abelian locally compact contraction groups.
