A note on the Boardman theorem (Q1273347)

Let \((T,M)\) be a smooth involution on a closed manifold with the fixed point set \(F\). A classical theorem of Boardman says that if \(5 \dim F < 2 \dim M\) then \((T,M)\) bounds as a manifold with involution. If \(2 \dim M \leq 5 \dim F\), the result does not necessarily hold. The paper under review considers the case in which \(2 \dim M \leq 5 \dim F\), and gives necessary and sufficient conditions for \((T,M)\) to bound. The conditions are given in terms of the fixed point data of \((T,M)\).