Semi-topological cycle theory I

Jyh-Haur Teh

Vol. 259 (2012), No. 1, 195–208

DOI: 10.2140/pjm.2012.259.195

Abstract

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

Keywords

Lawson homology, morphic cohomology, semi-topological varieties, Friedlander–Lawson moving lemma, Hilbert scheme, Chow varieties

Mathematical Subject Classification 2010

Primary: 14C25

Secondary: 19E15

Milestones

Received: 20 January 2010

Revised: 3 January 2012

Accepted: 26 July 2012

Published: 31 August 2012