不动点集为CP(2n)×HP(2m+1)的对合OA

In order to develop equivariant cobordism classification of manifolds with involutions whose fixed point sets are product of projective spaces,the equivariant cobordism classification of all manifolds with involutions(M,T)with fixed point set F=CP(2n)×HP(2m+1)(m≥n≥3)was studied.Firstly,the existence of bounding involutions with CP(2n)×HP(2m+1)as its fixed point set was proved;Secondly,according to the form of normal bundle over F,the results were discussed by dividing several cases,by constructing a suitable symmetric polynomial,according to Kosniowski-Stong theorem,the contradiction was obtained by calculating characteristic numbers,and non-existence of non-bounding involutions was proved,or that involutions exist and bordism was obtained by calculating characteristic numbers;Finally,bordism was obtained.The results show that every smooth closed manifold(M,T)with an involution T having fixed point set of form CP(2n)×HP(2m+1)(m≥n≥3)exists and bounds.The research results enrich the equivariant cobordism classification of involutions with fixed point set product of projective spaces,and provide theoretical reference for the further study involutions with fixed point set other special manifold.