Abstract
The restrictions on the topology of nonsingular plane projective real algebraic curves of odd degree, obtained by O. Viro and the author in the paper published in the early 90s, are extended to flexible curves lying on an almost complex four-dimensional manifold. Some examples of real algebraic surfaces and real curves on them prove the sharpness of the obtained inequalities. In addition, it is proved that a compact Lie group smooth action can be lifted to a cyclic branched covering space \(\tilde{X}\) over a closed four-dimensional manifold, and a sufficient condition for \(H_{1}(\tilde{X})=0\) was found.
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ACKNOWLEDGMENTS
The author is grateful to S. Yu. Orevkov for paying author’s attention at M. Manzaroli’s paper [2], for stating the problem and for useful discussions.
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The author’s work was done on a subject of the State assignment (no. 0729-2020-0055).
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(Submitted by I. Sh. Kalimullin)
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Zvonilov, V.I. Viro–Zvonilov Inequalities for Flexible Curves on an Almost Complex Four-Dimensional Manifold. Lobachevskii J Math 43, 720–727 (2022). https://doi.org/10.1134/S1995080222060348
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DOI: https://doi.org/10.1134/S1995080222060348