Involution number sequence and dimensions of components in fixed point set of involution (Q1201557)

Let \(M^ n\) be a smooth closed \(n\)-manifold, \((M^ n,T)\) a smooth unfree involution on \(M^ n\) and \(F^ k\) the disjoint union of all the \(k\)-dimensional components in the fixed point set \(F\) of the involution. The aim of this paper is to associate \((M^ n,T)\) with a number sequence and to prove that this sequence is precisely the strictly increasing arrangement of all the possible integers \(n-k\) in which \(F^ k\) is nonempty.