Journal of the European Mathematical Society
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Cycles on algebraic models of smooth manifoldsWojciech Kucharz (1) Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, 30-348 , Kraków, POLAND
Every compact smooth manifold $M$ is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of $M$. We study modulo $2$ homology classes represented by algebraic subsets of $X$, as $X$ runs through the class of all algebraic models of $M$. Our main result concerns the case where $M$ is a spin manifold.
Keywords: Real algebraic sets, algebraic cohomology classes, algebraic models
Kucharz W. Cycles on algebraic models of smooth manifolds. J. Eur. Math. Soc. 11 (2009), 393-405. doi: 10.4171/JEMS/154