Journal of the European Mathematical Society

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Volume 11, Issue 2, 2009, pp. 393–405
DOI: 10.4171/JEMS/154

Cycles on algebraic models of smooth manifolds

Wojciech Kucharz[1]

(1) Institute of Mathematics, Jagiellonian University, ul. Ɓojasiewicza 6, 30-348, KRAKOW, 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 Wojciech: Cycles on algebraic models of smooth manifolds. J. Eur. Math. Soc. 11 (2009), 393-405. doi: 10.4171/JEMS/154