COMPLEX CYCLES AS OBSTRUCTIONS ON REAL ALGEBRAIC VARIETIES

Abstract

AbstractLetYbe a compact nonsingular real algebraic variety of positive dimension. Then one can find a compact connected nonsingular real algebraic varietyX, which admits a continuous map intoYthat is not homotopic to any regular map. It is hard to determine the minimum dimension of such a varietyX. In this paper, new upper bounds for dimXare obtained. The main role in the constructions is played by complex algebraic cycles onY.