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arXiv · 2501.07907

Steenrod operations for $4$-dimensional toric orbifolds

Tseleung So
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Abstract

We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod-$2$ cohomology of 4-dimensional toric orbifolds. As applications, the stable homotopy type and the gauge groups of a $4$-dimensional toric orbifold are determined, a partial solution to the cohomological rigidity problem for $4$-dimensional toric orbifolds is provided, and, in the smooth case, a combinatorial criterion is established for when the toric orbifold is spin.

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Tseleung So. 2025-01-14. Steenrod operations for $4$-dimensional toric orbifolds. https://arxiv.org/abs/2501.07907

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