Geodesic
COMPLEX CYCLES AS OBSTRUCTIONS ON REAL ALGEBRAIC VARIETIES
Glasgow mathematical journal, Tome 57 (2015) no. 2, pp. 343-347

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Let Y be a compact nonsingular real algebraic variety of positive dimension. Then one can find a compact connected nonsingular real algebraic variety X, which admits a continuous map into Y that is not homotopic to any regular map. It is hard to determine the minimum dimension of such a variety X. In this paper, new upper bounds for dim X are obtained. The main role in the constructions is played by complex algebraic cycles on Y. 
KUCHARZ, WOJCIECH. COMPLEX CYCLES AS OBSTRUCTIONS ON REAL ALGEBRAIC VARIETIES. Glasgow mathematical journal, Tome 57 (2015) no. 2, pp. 343-347. doi: 10.1017/S0017089514000329
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     author = {KUCHARZ, WOJCIECH},
     title = {COMPLEX {CYCLES} {AS} {OBSTRUCTIONS} {ON} {REAL} {ALGEBRAIC} {VARIETIES}},
     journal = {Glasgow mathematical journal},
     pages = {343--347},
     year = {2015},
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     number = {2},
     doi = {10.1017/S0017089514000329},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000329/}
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