Abstract:

Let (M^r,T) be a smooth closed manifold of dimension r with a smooth involution T, we investigate the bordism classes of the involutions with the fixed point set F=RP₁(2m)∪RP₂(2m)∪RP(2n+1)(m≥1). Constructing symmetric polynomial and computing characteristic number, we have proved that if r>2m+2n+2, then every involution (M^r,T) fixing F bounds.

Key words: involution, fixed point set, characteristic class, bordism