A THEOREM ON THE ACTION OF SO(3)
Abstract
A proof is presented of the following theroem: Let X be a compact cohomology n-manifold over Z, the ring of integers, with H*(X;Z) equal to H*(S(n);Z) and let G equal SO(3), the rotational of the euclidean 3-space, act on X with B equal to (n-2), where B is the union of all singular orbits of dimension Z. Then D does not equal zero and one of the following occurs: (1) n equals one and G acts trivially on X; (2) n is greater than or equal to 4 and for every Y belonging to D,G(Y) is a dihedral group of order 4 (Y is an element of X); or (3) n is greater than or equal to 5, and for every Y belonging to U, G(Y) is the identity group.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1961
- Accession Number
- AD0264399
Entities
People
- Chung-tao Yang
Organizations
- University of Pennsylvania