# Integral and rational mapping classes

@article{Manin2020IntegralAR,
title={Integral and rational mapping classes},
author={F. Manin and S. Weinberger},
journal={Duke Mathematical Journal},
year={2020},
volume={169},
pages={1943-1969}
}
• Published 2020
• Mathematics
• Duke Mathematical Journal
Author(s): Manin, Fedor; Weinberger, Shmuel | Abstract: Let $X$ and $Y$ be finite complexes. When $Y$ is a nilpotent space, it has a rationalization $Y \to Y_{(0)}$ which is well-understood. Early on it was found that the induced map $[X,Y] \to [X,Y_{(0)}]$ on sets of mapping classes is finite-to-one. The sizes of the preimages need not be bounded; we show, however, that as the complexity (in a suitable sense) of a rational mapping class increases, these sizes are at most polynomial. This… Expand
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