Involutions fixing HP1(2m)∪HP2(2m)∪HP(2n+1) of the fixed point set

Abstract

Let (Mr,T) be a smooth closed manifold of dimension r with a smooth involution T whose fixed point set is F=HP1(2m)∪HP2(2m)∪HP(2n+1)(m≥1), where HP(n) denotes the n-dimensional quaternionic projective space. By constructing symmetric polynomial and computing characteristic number, it is proved that when r>8m+8n+8, every involution (Mr,T) fixes F bounds.

Keywords

• algebraic topology
• involution
• fixed point set
• characteristic class
• bordism