DIFFERENTIABLE ACTIONS ON HOMOTOPY SEVEN SPHERES, III.
Abstract
Denote by G the circle group of complex numbers of absolute value 1, by Z2 the subgroup of G of order 2 and by Z the group of integers. Further, denote by II an infinite cyclic group of equivariant diffeomorphism classes of free differentiable actions of G on homotopy 7-spheres. It has been shown that there is an isomorphism tau of Z onto II such that for an integer i, if a free differentiable action of G on a homotopy 7-sphere sigma sub i is in tau(i), then the first Pontrjagin class of the Orbit space sigma sub i/G is given by Pi(sigma sub i/G) = (24i + 4) a sub i to the second power where a sub i is a generator of H squared (sigma sub i/G;Z). It is known that sigma sub i has the ordinary differentiable structure if i = 0 or 6 mod 14. The purpose of this paper is to investigate the free differentiable actions of Z2 on sigma sub i obtained from the actions of G. Our main results is that the Browder-Livesay invariant of (Z2, sigma sub i) is equal to 8i so that for i not equal to j, (Z2, sigma sub i) and (Z2, sigma sub j) are not piecewise linearly equivalent. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0651967
Entities
People
- Chung-tao Yang
- D. Montgomery
Organizations
- University of Pennsylvania