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arXiv · 2311.15893

Determination of bounds on the dimension of manifolds with involutions fixing $F^n\cup F^4$

Arijit Nath·Avijit Nath
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Abstract

Let $M^m$ be an $m$-dimensional, smooth and closed manifold, equipped with a smooth involution $T\colon M^m \to M^m$ fixing submanifolds $F^n$ and $F^4$ of dimensions $n$ and $4$, respectively, where $4<n<m$ and $F^n\cup F^4$ does not bound. We determine the upper bound for $m$, for each $n$. The existence of these bounds is ensured by the famous Five Halves Theorem of J. Boardman, which establishes that, under the above hypotheses, $m\leqslant\frac{5}{2}n$.

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Arijit Nath, Avijit Nath. 2023-11-27. Determination of bounds on the dimension of manifolds with involutions fixing $F^n\cup F^4$. https://arxiv.org/abs/2311.15893

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