### Leibniz Homology, Characteristic Classes and K-theory, by Jerry M. Lodder

In this paper we identify many striking elements in Leibniz
(co)homology which arise from characteristic classes and K-theory.
For a group G and a field k of characteristic zero, it is shown that all
primary characteristic classes, i.e., H^{*}(BG;k), naturally inject
into certain Leibniz cohomology groups via an explicit chain map.
Moreover, if f: A --> B is a homomorphism of algebras or rings, the
relative Leibniz homology groups HL_{*}(f) are defined, and if in
addition f is surjective with nilpotent kernel, A and B algebras
over the rationals, then there is a natural surjection
HL_{*+1}(gl(f)) --> HC_{*}(f),
where HC_{*}(f) denotes relative cyclic homology, and gl(f): gl(A)
--> gl(B) is the induced map on matrices. Here again, the above
surjection is realized via an explicit chain map, and offers a
relation between Leibniz homology and K-theory.

Jerry M. Lodder <jlodder@nmsu.edu>