Classifying involutions on \(PR(2k)\) up to equivariant cobordism
The main result of this paper is that up to equivariant bordism, every involution \((RP(2k),T)\) on an even projective space is equivalent to one of the standard linear involutions \(T_ i([x_ 0,\dots,x_{2k}])= [- x_ 0,\dots,-x_ i, x_{i+1},\dots, x_{2k}]\) with \(-1\leq i\leq k- 1\), where \(T_{-1}\) = identity. While the proof given here is based entirely on bordism methods, the result is an immediate consequence of Smith theory. It is well-known that the fixed set of any involution on \(RP(2k)\) has the same \(\text{mod} 2\) cohomology as one of the linear examples.
scientific article; zbMATH DE number 205748
scientific article