S^(1)×S^(3)作用下的同伦不动点集的有理同伦型  

The Rational Homotopy Type of Homotopy Fixed Point Sets of S^(1)×S^(3) Actions

作　　者：谢桑 Xie Sang(School uf Mathematical Sciences,Na?ikui University,Tianjin 300071,China)

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《南开大学学报（自然科学版）》2022年第1期8-14,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported in part by the National Natural Science Foundation of China (12171165);Tianjin Natural Science Foundation (19JCYBJC30200)。

摘　　要：确定了S^(1)×S^(3)作用在特定有理复形上的同伦不动点集的有理同伦型;证明了某一类空间M椭圆等价于其同伦不动点集Mh(S^(1)×S^(3))的任意连通分支椭圆.The rational homotopy type of the homotopy fixed point sets of S^(1)×S^(3)-actions is determined on some rational complexes.Moreover,it’s shown that M is elliptic if and only if one of the path components of the homotopy fixed point set Mh(S^(1)×S^(3))is elliptic under certain conditions.

关 键 词：同伦不动点集 有理同伦论 椭圆空间 

分 类 号：O189.2[理学—数学]