Algebraicity of cycles on smooth manifolds

Bibliographic description

punktacja MEiN [2011 A]: 35

title:	Algebraicity of cycles on smooth manifolds
author:	Kucharz Wojciech
journal title:	Selecta Mathematica. New Series
volume:	17
issue:	4
date of publication :	2011
pages:	855-878
ISSN:	1022-1824
eISSN:	1420-9020
DOI:	10.1007/s00029-011-0064-0
language:	English
journal language:	English
abstract in English:	According to the Nash-Tognoli theorem, each compact smooth manifold M is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of M. It is interesting to investigate to what extent algebraic and differential topology of compact smooth manifolds can be transferred into the algebraic-geometric setting. Many results, examples and counterexamples depend on the detailed study of the homology classes represented by algebraic subsets of X, as X runs through the class of all algebraic models of M. The present paper contains several new results concerning such algebraic homology classes. In particular, a complete solution in codimension 2 and strong results in codimensions 3 and 4.
keywords in English:	real algebraic set, algebraic homology class, algebraic model of a smooth manifold
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper