Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove...Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove that I(T)is precisely the strictly increasing arrange-ment of all the possible integers n-k in which F^k is nonempty, F^k being the disjointunion of all the k-dimensional components in the fixed point set F of the involution (M^n,T). For application, we shall give a proof for the well-known fact that the fixed point set ofa smooth unfree involution on S^n must be a constant-dimensional smooth closed submanifoldof S^n.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Given a smooth unfree involution (M^n, T), where M^n is a smooth closed n-manifold, weshall associate (M^n, T) with a number sequence I(T), called the involution number sequenceassociated with (M^n, T). We shall prove that I(T)is precisely the strictly increasing arrange-ment of all the possible integers n-k in which F^k is nonempty, F^k being the disjointunion of all the k-dimensional components in the fixed point set F of the involution (M^n,T). For application, we shall give a proof for the well-known fact that the fixed point set ofa smooth unfree involution on S^n must be a constant-dimensional smooth closed submanifoldof S^n.
