Commuting involutions with fixed point set of variable codimension (Q5946542)

This paper considers the group \(J=J_{n,k} (l_1,\dots,l_m)\) of cobordism classes of \(n\)-dimensional manifolds which admit an action of \((\mathbb{Z}_2)^k\), \(k\geq 2\), having fixed components of codimensions the \(l_i\). Under various conditions it is shown that \(J\) is all cobordism classes of \(n\)-dimensional manifolds (when some \(l\) is even) or all classes with even Euler characteristic (when all \(l\) are odd). The choices of conditions are all rather technical.