### Semi-topological K-homology and Thomason's Theorem, by Mark E. Walker

In this paper, we introduce the "semi-topological K-homology" of
complex varieties, a theory related to semi-topological K-theory much
as connective topological K-homology is related to connective
topological K-theory. Our main theorem is that the semi-topological
K-homology of a smooth, quasi-projective complex variety Y coincides
with the connective topological K-homology of the analytic space
associated to Y. From this result, we deduce a pair of results
relating semi-topological K-theory with connective topological
K-theory. In particular, we prove that the "Bott inverted"
semi-topological K-theory of a smooth, projective complex variety X
coincides with the topological K-theory of its analytic
realization. In combination with a result of Friedlander and the
author, this gives a new proof, in the special case of smooth,
projective complex varieties, of Thomason's celebrated theorem that
"Bott inverted" algebraic K-theory with finite coefficients coincides
with topological K-theory with finite coefficients.

Mark E. Walker <mwalker@math.unl.edu>