On homology of real algebraic sets
type: Item
instance of: scholarly article
title: On homology of real algebraic sets
zbMATH Open document ID: 0547.14018
DOI: 10.1007/BF01394776
author: Wojciech Kucharz
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143274
review text: Given a compact, connected, smooth (i.e. \(C^{\infty})\) surface, not diffeomorphic to the two-sphere, real projective plane, or Klein bottle, we construct a nonsingular real algebraic surface diffeomorphic to it whose first homology group with coefficients in the integers modulo 2 is not generated by algebraic cycles. Such algebraic surfaces diffeomorphic to smooth, orientable surfaces of positive genus \(\leq 9\) and of genus 1 have previously been found by Risler and Silhol, respectively [\textit{J. J. Risler}, Géométrie algébrique réelle et formes quadratiques, Journ. S.M.F., Univ. Rennes 1981, Lect. Notes Math. 959, 381-385 (1982; Zbl 0503.14014) and \textit{R. Silhol}, ibid. 443-450 (1982)]. The higher dimensional case is also considered.
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57R95
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 3871542
zbMATH Keywords: real algebraic sets
zbMATH Keywords: compact surface
zbMATH Keywords: first homology group
zbMATH Keywords: not generated by algebraic cycles
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3871542