\((\mathbb{Z}_2)^k\)-actions with disconnected fixed point set (Q5939841)

Let \(M^n\) be an \(n\)-dimensional manifold with \((\mathbb{Z}_2)^k\)-action. This paper introduces a linear independence condition for the fixed-point set of the action and shows that if each \(n-h\) dimensional part of the fixed set satisfies linear independence and \(\dim M>(2^{k+1}-1)\dim F\) then the action on \(M\) bounds. Previous results of this type had always needed the assumption that the \(n-h\) dimensional part of the fixed set was connected.