（Z_2）～k作用下的不动点集的信息为？时的一个必要条件
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摘要
设（Z_2）~k作用于光滑闭流形M~n上，其不动点集具有常余维数
（2~k-1），法丛分解为。本文利用Kosniowski-Stong公式得出
它的一个必要条件。
（Z_2）~2作用于光滑闭流形M~n上，其不动点集具有常余维数3，法
丛分解为p＝｛（2，1，0，（2，0，1），（1，1，1）｝。J~3_(n,2)（p）是具有上述性质的未定
向的n维上协边类［M~n］构成的集合。本文通过构造上协边环MO_*
的一组生成元决定了J~3_(n,2)（p）的群结构。
Let M~n be a closed smooth n-manifold, and it admits a (Z_2)~k-action with fixed point set data . By Kosniowski-Stong formula we get a
necessary condition.
Special generators of the unoriented cobordism ring MO, are constructed to determine the group J~3_(n,2)(p) of n-dimensional cobordism classes in MO_n containing a representative M~n admitting a (Z_2)~2-action with fixed point set of constant codimension 3, p = {(2,1,0), (2,0,1), (1,1,1)}.
（2~k-1），法丛分解为。本文利用Kosniowski-Stong公式得出
它的一个必要条件。
（Z_2）~2作用于光滑闭流形M~n上，其不动点集具有常余维数3，法
丛分解为p＝｛（2，1，0，（2，0，1），（1，1，1）｝。J~3_(n,2)（p）是具有上述性质的未定
向的n维上协边类［M~n］构成的集合。本文通过构造上协边环MO_*
的一组生成元决定了J~3_(n,2)（p）的群结构。
Let M~n be a closed smooth n-manifold, and it admits a (Z_2)~k-action with fixed point set data . By Kosniowski-Stong formula we get a
necessary condition.
Special generators of the unoriented cobordism ring MO, are constructed to determine the group J~3_(n,2)(p) of n-dimensional cobordism classes in MO_n containing a representative M~n admitting a (Z_2)~2-action with fixed point set of constant codimension 3, p = {(2,1,0), (2,0,1), (1,1,1)}.
引文
[1] P.E. Conner,Differentiable periodic maps (second edition), Lecture Notes in Math.Vol 738,Berlin:Springer Verlag,1979．
[2] P.L.Q. Pergher,(Z_2) ~k-actions with fixed point set of constant codimen-sion,Topology Appl,1992 46(1) :55-64．
[3] Jr. R.J. Shaker,Constant codimension fixed point sets of commuting involutions, Proc Amer Math Soc,1994,121(1) :275-281．
[4] Jr. R.J. Shaker,Dold manifolds with (Z_2) ~k-actions, Proc Amer Math Soc, 1995, 123(3) :955-958．
[5] R.E. Stong,On fibering of cobordism classes,Trans Amer Math Soc, 1973, 178(451) :431-447．
[6] C. Kosniowski,R.E. Stong,(Z_2) ~k-actions and characteristic numbers,Indiana Univ Math J, 1979,28(5) :725-743．
[2] P.L.Q. Pergher,(Z_2) ~k-actions with fixed point set of constant codimen-sion,Topology Appl,1992 46(1) :55-64．
[3] Jr. R.J. Shaker,Constant codimension fixed point sets of commuting involutions, Proc Amer Math Soc,1994,121(1) :275-281．
[4] Jr. R.J. Shaker,Dold manifolds with (Z_2) ~k-actions, Proc Amer Math Soc, 1995, 123(3) :955-958．
[5] R.E. Stong,On fibering of cobordism classes,Trans Amer Math Soc, 1973, 178(451) :431-447．
[6] C. Kosniowski,R.E. Stong,(Z_2) ~k-actions and characteristic numbers,Indiana Univ Math J, 1979,28(5) :725-743．