Proceedings of the American Mathematical Society

Author(s): Yildiray Ozan
Journal: Proc. Amer. Math. Soc. 129 (2001), 3167-3175.
MSC (1991): Primary 14P25; Secondary 14E05
Posted: April 9, 2001
Retrieve article in: PDF
This article is available free of charge

Let

be a commutative ring with unity and

-oriented compact nonsingular real algebraic variety of dimension

. If $i :X \rightarrow X_{\mathbb C}$ is any nonsingular complexification of

, then the kernel, which we will denote by

, 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

and give some of its applications.

1.: Akbulut, S., King, H.: Topology of real algebraic sets, M.S.R.I. book series, Springer, New York, 1992. MR 94m:57001
2.: -----: The topology of real algebraic sets, Enseign. Math. 29 (1983), 221-261. MR 86d:14016b
3.: -----: Transcendental submanifolds of ${\mathbb R}^n$ , Comment. Math. Helvetici 68 (1993), 308-318. MR 94j:57032
4.: Arnold, V. I.: The situation of ovals of real algebraic plane curves, involutions on 4-dimensional smooth manifolds, and the arithmetic of integral quadratic forms, Funktional Anal. i Prilozhen. 5 (1971), no.3, 1-9; English translation, Functional Anal. Appl. 5 (1971). MR 44:3999
5.: Bierstone E., Milman P.: Canonical desingularization in characteristic zero by blowing up the maximal strata of a local invariant, Invent. Math. 128 (1997), 207-302. MR 98e:14010
6.: Bochnak, J., Buchner, M., Kucharz, W.: Vector bundles over real algebraic varieties, K-Theory J. 3 (1989), 271-289. MR 91b:14075
7.: Bochnak, J., Coste, M., Roy, M.F.: Real Algebraic Geometry, Ergebnisse der Math. vol. 36, Springer, Berlin, 1998. MR 2000a:14067
8.: Bochnak, J., Kucharz, W.: A characterization of dividing real algebraic curves, Topology 35 (1996), 451-455. MR 97d:14082
9.: -----: On real algebraic morphisms into even-dimensional spheres, Ann. of Math., 128 (1988), 415-433. MR 89k:57060
10.: -----: On dividing real algebraic varieities, Math. Proc. Camb. Phil. Soc., 123 (1998), 263-271. MR 98m:14055
11.: Bredon, G. E.: Topology and Geometry, Springer, New York (1993). MR 94d:55001
12.: Dovermann, K. H.: Equivariant algebraic realization of smooth manifolds and vector bundles, Contemp. Math. 182 (1995), 11-28. MR 96a:57079
13.: Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. 79 (1964), 109-326. MR 33:7333
14.: Huisman, J.: The underlying real algebraic structure of complex elliptic curves, Math. Ann. 294 (1992), 19-35. MR 93i:14029
15.: Klein, F.: Über eine neue Art von Riemannischen Flachen, Math. Ann. 10 (1876), 398-416.
16.: Kulkarni, R. S.: On complexifications of differentiable manifolds, Invent. Math. J. 44 (1978), 49-64. MR 57:724
17.: Ozan, Y.: On entire rational maps in real algebraic geometry, Michigan Math. J. 42 (1995), 141-145. MR 96b:14070
18.: -----: Homology of real algebraic fiber bundles having circle as fiber or base, Michigan Math. J. 46 (1999), 113-121. MR 2000b:14082
19.: -----: An obstruction to finding algebraic models for smooth manifolds with prescribed algebraic submanifolds (to appear in Proc. Camb. Phil. Soc.).
20.: -----: On algebraic K-theory of real algebraic varieities with circle action (preprint).
21.: Rokhlin, V. A.: Complex orientations of real algebraic curves, Funktional Anal. i Prilozhen. 8 (1974), no. 3, 71-75; English translation, Functional Anal. Appl. 8 (1974). MR 51:4286
22.: -----: Complex topological characteristics of real algebraic curves, Uspekhi Mat. Nauk 33 (1978), no. 5, 77-89; English transl. in Russian Math. Surveys 33 (1978). MR 81m:14024
23.: Viro, O.: Topology of manifolds and varieties, Advances in Soviet Mathematics, American Mathematical Soc. Vol. 18, (1994). MR 95d:57001

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14P25, 14E05

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS