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Let $M^m$ be an $m$-dimensional, smooth and closed manifold, equipped with asmooth involution $T\colon M^m \to M^m$ fixing submanifolds $F^n$ and $F^4$ ofdimensions $n$ and $4$, respectively, where $4<n<m$ and $F^n\cup F^4$ does notbound. We determine the upper bound for $m$, for each $n$. The existence ofthese bounds is ensured by the famous Five Halves Theorem of J. Boardman, whichestablishes that, under the above hypotheses, $m\leqslant\frac{5}{2}n$.

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