Abstract
For $k\in\{2,3\}$ we classify endomorphisms of $H^*(G_{k,n};\mathbb Z_2)$ that commute with Steenrod squares (here, $G_{k,n}$ denotes the Grassmann manifold of $k$-dimensional subspaces in $\mathbb R^{n+k}$). Additionally, for all positive integers $k$ and $n$ we classify endomorphisms of $H^*(G_{k,n};\mathbb Z_2)$ that commute with Steenrod squares and such that the image of each class is a polynomial in the (nonzero) class of $H^1(G_{k,n};\mathbb Z_2)$.
Citation
Matej Milićević. Marko Radovanović. "Endomorphisms of real Grassmannians that commute with Steenrod squares." Bull. Belg. Math. Soc. Simon Stevin 29 (4) 471 - 490, december 2022. https://doi.org/10.36045/j.bbms.211212
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