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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On homology of real algebraic varieties


Author: Yildiray Ozan
Journal: Proc. Amer. Math. Soc. 129 (2001), 3167-3175
MSC (1991): Primary 14P25; Secondary 14E05
Published electronically: April 9, 2001
MathSciNet review: 1844989
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Abstract:

Let $R$ be a commutative ring with unity and $X$ an $R$-oriented compact nonsingular real algebraic variety of dimension $n$. If $i :X \rightarrow X_{\mathbb C}$ is any nonsingular complexification of $X$, then the kernel, which we will denote by $KH_k(X, R)$, of the induced homomorphism ${i}_*:H_k(X,R) \rightarrow H_k(X_{\mathbb C},R)$ is independent of the complexification. In this work, we study $KH_k(X, R)$ and give some of its applications.


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Additional Information

Yildiray Ozan
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: ozan@metu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06065-8
PII: S 0002-9939(01)06065-8
Keywords: Real algebraic varieties, algebraic homology, entire rational maps
Received by editor(s): November 26, 1998
Received by editor(s) in revised form: March 20, 2000
Published electronically: April 9, 2001
Communicated by: Michael Stillman
Article copyright: © Copyright 2001 American Mathematical Society