【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.更多还原

【Abstract】 Let Mn be a closed smooth manifold and T:Z2×Mn→ Mn denote a smooth action of the integral additive group Z2 on Mn which is called involution.The fixed point set F of T is the disjoint union of closed manifold Mn,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 manifolds and let Jkn 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 Jkn is a subgroup of Rn and that Jk*=∑∞n=kJkn is an ideal of the unoriented bordism ring R*=∑nRn.The case k=10 by means of constructing the generators of R* is discussed.更多还原