常余维数为10的带对合流形  

Manifolds with Involutions of Codimension Ten

作　　者：马凯[1] 王冲[2] 李日成[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050016 [2]沧州师范专科学校数学系,河北沧州061001

出　　处：《河北师范大学学报（自然科学版）》2009年第4期440-447,共8页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(10371029);河北省自然科学基金(103144);河北师范大学博士基金(L2005B03)

摘　　要：设Mn是n维光滑闭流形,T:Z2×Mn→Mn是整数加群Z2在Mn上的光滑作用,简称为对合.其不动点集F是Mn的有限个闭子流形的不交并.若F的每个分支都具有常维数n-k,则称F具有常余维数k.记Rn为所有n维光滑闭流形的未定向上协边类作成的群.Jnk是它的子集,其中每个未定向上协边类都有不动点集常余维数为k的带对合光滑闭流形作为其代表元.易知,Jkn是Rn的子群,Jk*=∑∞n=kJnk是上协边环R*=∑nRn的一个理想.通过构造R*的生成元对k=10的情形进行了研究.Let M^n be a closed smooth manifold and W：Z2 × M^n→ M^n denote a smooth action of the integral additive group Z2 on M＂ which is called involution. The fixed point set F of T is the disjoint union of closed manifold M,,, which are finite in number. If each componentof F is of constant dimension n - k, we say that F is of constant codimension k. Let Rn be the group of unoriented bordism class of n-dimensional smooth manifoldsand let j n k be its subset consisting of the classes which are represented by manifolds admitting smooth involutions with fixed point set of constant codimension k. It is easy to see that Jnk. is a subgroup of Rn, and that Jk＊=∑∞n=kJnk is an ideal of the unoriented bordism ring R＊=∑nRn, The case k = 10 by means of constructing the generators of R is discussed.

关 键 词：对合 上协边类 射影空间丛 

分 类 号：O189.3[理学—数学]