acase@tulane.edu

It is known in general the homotopy type and simple homotopy type are different except possibly in dimension 2. In this paper, we show that in dimension 2 homotopy type and simple homotopy type are the same when the fundamental group of the finite 2-dimensional complexes is finite and abelian The technique used is to show that all of the elements of the Whitehead group of a complex K are realizable as torsions of self-equivalences on K Due to the work of Wolfgang Metzler, the above technique will not work if the fundamental group is not finite We display an example of a finite 2-dimensional complex where the fundamental group is finite but not abelian, and where not all of the Whitehead group is realizable as the torsions of self-equivalences which induce the identity map on the fundamental group / acase@tulane.edu

In this dissertation, we establish the existence of new types of indecomposable modules over valuation domains in the following two settings: (1) Finitely generated modules. Given a pair of positive integers m $<$ n and a suitable valuation domain R, we construct finitely generated indecomposable R-modules M of length n and of Goldie dimension m such that the endomorphism ring of M is local. (2) Finite rank torsion-free modules. Given a pair of positive integers m $<$ n and a suitable valuation domain R, we construct finite rank torsion-free indecomposable R-modules M of rank n with basic submodules of rank m such that the endomorphism ring of M is local / acase@tulane.edu

The research objective of this work is development of statistical methodology for identifying 'non-tracking' individuals through their longitudinal observations. Non-tracking individuals are those whose patterns of change over time differs qualitatively from that of most other individuals in the population Following methods developed by Rao, patterns of change over time are modeled as linear combinations of optimally chosen orthogonal vectors. Non-trackers are defined as individuals requiring more than the usual number of vectors to fit their set of observations. The Akaike Information Criterion is used to determine the number of vectors required by each individual, and hence to identify the nontrackers. The statistical methodology developed is applied to simulated data to study the reliability of the method. It is also applied to longitudinal observations of cardiovascular disease risk factor variables measured in children. Height, systolic blood pressure and serum total cholesterol were analyzed. In general, children 5-17 years of age track for these variables. The number of vectors fitted for each age cohort showed the methodology correctly modeled important biologic events such as the height growth spurt in children / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

It is known that an h-cobordism from M #(,r)(S('p) x S('q)), dim M (GREATERTHEQ) 5, 2 (LESSTHEQ) p (LESSTHEQ) dim M-2 is inertial provided the torsion of the h-cobordism can be represented by an r x r matrix. In this paper we generalize this result and show that, in fact, the h-cobordism can be surgered to a product cobordism. The techniques do not involve the surgery obstruction groups of C.T.C. Wall as the above class contains h-cobordisms for which the surgery obstruction element associated to the h-cobordism by means of the Rothenberg sequence is non-zero We introduce an algebraic condition on the torsion of the h-cobordism which guarantees the h-cobordism is inertial provided the dimension of the h-cobordism is 7 or 15. Here again the h-cobordism can be surgered to a product cobordism, and the techniques do not involve the surgery obstruction groups of C.T.C. Wall. These groups take into account only those properties possessed by all manifolds which differ by 4n dimensions whereas the techniques here rely on the fact that the dimension of the h-cobordism is 7 or 15 Finally, if the torsion of the h-cobordism (W;M,N) satisfies (tau) = (-1)('dim) ('W)(tau)*, for M(,0) a codimension one submanifold of M having the same fundamental group, N is obtained from M by splitting along M(,0) and regluing by an isomorphism h which is described geometrically for a class of h-cobordisms characterized by an algebraic condition on the torsion, provided the dimension of the h-cobordism is 2n + 1, n (GREATERTHEQ) 3 / acase@tulane.edu

In this dissertation, we construct a Baer sum for group coextensions and an interpretation of the $n\sp{th}$ Leech cohomology group in terms of extensions in a suitable functor category / acase@tulane.edu

acase@tulane.edu