不动点集为Dold流形P(2,15)的对合

为了研究不动点集为Dold流形的对合的等变协边分类，针对一个特定的Dold流形F=P(2,15),确定了以F为不动点集的所有带对合的流形(M,T)的等变协边分类。首先，给出了P(2,15)上切丛和法丛的Stiefel-Whitney示性类。其次，根据Kosniowski-Stong定理，构造合适的对称多项式函数，出现矛盾，证明假设错误，对合不存在；或者证明对任意对称多项式函数都满足Kosniowski-Stong定理，说明对合的存在性。最后，得到以P(2,15)为不动点集的对合(M,T)协边。结果表明，存在以F=P(2,15)不动点集的对合，且能够确定对合的等变协边分类。研究结果推广了不动点集为F=P(2,n)(n=1,3,5)的对合的研究结论，丰富了不动点集为Dold流形的对合的等变协边分类问题，也为研究不动点集其他特殊流形的对合提供了借鉴和参考。

Involutions with fixed point set Dold manifold P(2,15)

In order to study the equivariant cobordism classification of involutions with fixed point set Dold manifolds, for a special Dold manifold WTBX]F=PDK](2,15), the equivariant cobordism classification of all involutions (M,T) with fixed point set was determined. Firstly, the Stiefel-Whitney classes of tangent bundle and normal bundle over PDK](2,15) were given. Secondly, according to Kosniowski-Stong Theorem, either the contradiction was obtained by constructing a suitable symmetric polynomial function to prove that the hypothesis was wrong and the involution did not exist, or that arbitrary symmetric polynomial functions satisfy Kosniowski-Stong Theorem was proved, which illustrate the existence of involution. Finally, every involution (M,T) with fixed point set PDK](2,15) bounds was obtained. The results show that there exists an involution with fixed point set PDK](2,15), and the equivariant cobordism classification of all involutions can be determined. The research results popularize the conclusion of studying involutions fixing F=PDK](2,n)(n=1,3,5), enrich the equivariant cobordism classification of involutions with fixed point set Dold manifolds, and provide some reference for researching involutions of fixed point set with other special manifold.