×

Introduction to Lawson homology. (English) Zbl 1066.14023

Müller-Stach, S. (ed.) et al., Transcendental aspects of algebraic cycles. Proceedings of the Grenoble summer school, Grenoble, France, June 18–July 6, 2001. Cambridge: Cambridge University Press (ISBN 0-521-54547-1/pbk). Mathematical Society Lecture Note Series 313, 44-71 (2004).
This paper is meant to serve as a concise introduction to Lawson homology of projective varieties. It is organized as follows. In the first section the authors recall some basic topological tools needed for a first definition of Lawson homology (homotopy groups, Eilenberg-Mac Lane spaces, Hurewicz theorem, Lawson’s suspension theorem). Then some basic examples are discussed. In the second section they discuss the topology of ‘cycle spaces’ in order to understand functoriality of Lawson homology. In the third and final section they relate various equivalent definitions.
For the entire collection see [Zbl 1050.14002].

MSC:

14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14C25 Algebraic cycles
PDFBibTeX XMLCite