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不动点集为RP₁（2m）∪RP₂（2m）∪RP（2n+1）的对合

Involutions Fixing RP₁（2m）∪RP₂（2m）∪RP（2n+1）

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【Author】 ZHAO Su-qian1,DING Yan-hong2(1.College of Basic Science,Hebei University of Science and Technology,Shijiazhuang 050018,China; 2.College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050016,China)

【机构】河北科技大学理学院；河北师范大学数学与信息科学学院；

【摘要】设(Mr,T)是一个带有光滑对合T的r维光滑闭流形,考虑当对合的不动点集为F=RP1(2m)∪RP2(2m)∪RP(2n+1)(m≥1)时对合的协边分类.通过构造合适的对称多项式和计算示性数,证明了若r>2m+2n+2,则每个以F为不动点集的对合(Mr,T)协边.更多还原

【Abstract】 Let(Mr,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(Mr,T) fixing F bounds.更多还原