Cycles on algebraic models of smooth manifolds
type: Item
instance of: scholarly article
title: Cycles on algebraic models of smooth manifolds
zbMATH Open document ID: 1160.14045
DOI: 10.4171/JEMS/154
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2009-04-21T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: Summary: Every compact smooth manifold \(M\) is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of \(M\). We study modulo 2 homology classes represented by algebraic subsets of \(X\), as \(X\) runs through the class of all algebraic models of \(M\). Our main result concerns the case where \(M\) is a spin manifold.
Mathematics Subject Classification ID: 14P05
Mathematics Subject Classification ID: 14P25
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 5545784
zbMATH Keywords: real algebraic sets
zbMATH Keywords: algebraic cohomology classes
zbMATH Keywords: algebraic models
author: Wojciech Kucharz
MaRDI profile type: Publication
cites work: The topology of real algebraic sets
cites work: Q4002664
cites work: Q3338378
cites work: Q3916680
cites work: Q3854334
cites work: Q3963140
cites work: Q4210476
cites work: Algebraic models of smooth manifolds
cites work: K-theory of real algebraic surfaces and threefolds
cites work: Algebraic Cycles and Approximation Theorems in Real Algebraic Geometry
cites work: Q4233738
cites work: La classe d'homologie fondamentale d'un espace analytique
cites work: Differentiable periodic maps. 2nd ed
cites work: On homology of real algebraic sets
cites work: Algebraic Equivalence and Homology Classes of Real Algebraic Cycles
cites work: Algebraic cycles and algebraic models of smooth manifolds
cites work: Characteristic Classes. (AM-76)
cites work: Real algebraic manifolds
cites work: Q3969056
cites work: Q3222961
cites work: Q4321743
cites work: Q5679473
cites work: Q3906130
OpenAlex ID: W2039959418
Recommended article: Algebraic cycles and algebraic models of smooth manifolds
Recommended article: Complex cycles on algebraic models of smooth manifolds
Recommended article: Algebraicity of cycles on smooth manifolds
Recommended article: Algebraic equivalence of cycles and algebraic models of smooth manifolds
Recommended article: Complex Cycles on Real Algebraic Models of a Smooth Manifold
Recommended article: Cycles on Nash algebraic models of smooth manifolds
Recommended article: Algebraic models of smooth manifolds
Recommended article: Cycles, curves and vector bundles on an algebraic surface
Recommended article: Algebraic cycles and fibrations
Recommended article: Cyclic homology of algebraic hypersurfaces
description: scientific article; zbMATH DE number 5545784