On homology of real algebraic sets
Copyright policy )On homology of real algebraic sets
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.
- DigiZeitschriften Germany
- University of New Mexico United States
compact surface, 510.mathematics, not generated by algebraic cycles, Topology of the Euclidean \(2\)-space, \(2\)-manifolds, Real algebraic and real-analytic geometry, Realizing cycles by submanifolds, Algebraic topology on manifolds and differential topology, first homology group, real algebraic sets, Article
compact surface, 510.mathematics, not generated by algebraic cycles, Topology of the Euclidean \(2\)-space, \(2\)-manifolds, Real algebraic and real-analytic geometry, Realizing cycles by submanifolds, Algebraic topology on manifolds and differential topology, first homology group, real algebraic sets, Article
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