In all that follows, D denotes a monoid whose underlying space is an n-disk, H a compact group of units of D, and A a compact group of monoid automorphisms of D. This thesis is primarily concerned with the structure of H, Z(H,D) = {d (ELEM) D (VBAR) hd = dh for all h (ELEM) H} and F(A,D) = {d (ELEM) D (VBAR) (eta) (d) = d for all (eta) (ELEM) A} for small values of n One of the primary tools that we develop for this thesis is the following theorem: If A acts effectively on D (or any monoid whose underlying space is an orientable manifold with connected boundary), then A restricts to an effective action on (PAR-DIFF)D For the case that n (LESSTHEQ) 3, we show that Z(H,D) and F(A,D) are disks and H is represented as an abelian subgroup of O(n). When n = 4, we restrict our attention to the case where H is a Lie group. We show, with the possible exception of two finite non-solvable groups, that Z(H,D) is a (generalized) disk. By studying the center of H and the Sylow subgroups of H, we derive a strong relationship between non-abelian groups of units and subgroups of O(2) and S('3) We also develop some techniques for constructing examples that complement the theory / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_23947 |
| Date | January 1981 |
| Contributors | Castellano, Bruno Michael (Author) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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