Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds

Mauricio Bustamante; Bena Tshishiku

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arXiv · 2408.09346

Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds

Mauricio Bustamante·Bena Tshishiku

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Abstract

We introduce an invariant of a pair of commuting invertible matrices that we call the rotation index. We apply this invariant, together with the Milnor--Munkres--Novikov pairing, to the study of some questions about group actions of $\mathbb{Z}^2$, specifically the Nielsen realization problem, higher-rank Anosov actions, and extending actions from the sphere $S^{d-1}$ to the disk $D^d$.

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Mauricio Bustamante, Bena Tshishiku. 2024-08-18. Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds. https://arxiv.org/abs/2408.09346

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