Doctoral Dissertations
Date of Award
8-1989
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Mathematics
Major Professor
Lawrence S. Husch
Committee Members
Carl G. Wagner, Robert Daverman, Morwen Thistlethwaite, Mary Sue Younger
Abstract
The lens space Ln,k may be constructed by identifying certain pairs of faces of the suspension of a regular n-gon, so that the cone points are glued together. If the faces are paired together as in the construction of Ln,k but the faces are identified with a twist, the resulting complex will be a three-manifold for certain k. Many of these manifolds are shown to be of distinct homotopy type, by an analysis of the number of distinct, irreducible representations of the fundamental group into SO(3).
These manifolds are shown to be Seifert fibered, and are completely distinguished by an analysis of the base orbifold structure. Further, they are shown to be homeomorphic to the cyclic covers of S3, branched over the trefoil knot.
This geometric procedure generalizes to construct other classes of manifolds, including certain Brieskorn manifolds— namely, the cyclic coverings of S3, branched over an arbitrary torus knot. By similar methods, many of these manifolds are also shown to be distinct. In particular, it is shown that the cyclic covers of S3, branched over a fixed torus knot, are distinct.
Recommended Citation
Emert, John Wesley, "Defining and distinguishing "Twisted" lens spaces. " PhD diss., University of Tennessee, 1989.
https://trace.tennessee.edu/utk_graddiss/11642
