Semi-topological cycle theory I

TL;DR

This paper extends algebraic cycle theories to semi-topological varieties, establishing fundamental theorems like suspension, splitting, and duality, and constructs K-groups and Chern classes in this new context.

Contribution

It introduces a semi-topological cycle framework, proving key theorems and constructing K-groups and Chern classes, advancing the understanding of algebraic cycles in topological settings.

Findings

Lawson suspension and splitting theorems proved

A duality theorem between Lawson homology and morphic cohomology established

K-groups and Chern classes constructed for semi-topological varieties

Abstract

We study algebraic varieties parametrized by topological spaces and enlarge the domains of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and splitting theorem. A version of Friedlander-Lawson moving is obtained to prove a duality theorem between Lawson homology and morphic for smooth semi-topological projective varieties. K-groups for semi-topological projective varieties and Chern classes are also constructed.