Study of intersections and links on non-simply-connected equivariant manifolds and K-theory

设G是有限群，X和Y是光滑G-流形。给定一个从X到Y的G-映射f，存在一个代数元素(障碍类)，它决定是否可以通过X上的G-手术将f转换为同伦等价g。X的k次同伦群的元素与(k-1)维元素之间的交集(分别对于G的子群H，我们给出了一个删除/插入X中不动点集的G-运算理论，作为它的应用，我们构造了各种和许多新的Smith等价的实G-表示空间对。

Let G be a finite group, and let X and Y be smooth G-manifolds. Given a G-map f from X to Y, there is an algebraic element (obstruction class) which determines whether one can convert f to a homotopy equivalence g by G-surgeries on X. In this research, considering links (resp. intersections) between elements of the k-th homotopy group of X and (k-1)-dimensional (resp. k-dimensional) H-fixed point sets of X for subgroups H of G, we gave a G-surgery theory to delete /insert fixed point sets in X. As applications of it, we construct various and many new pairs of Smith-equivalent real G-representation spaces.