No abstract

We study the algebraic topology of configuration spaces as interesting objects in their own right and with the goal of constructing invariants for topological manifolds. We calculate the complete Massey product structure for the universal cover of the space of two point configurations in a three-dimensional lens space. We then construct rational homotopy models for these spaces and calculate the rational homotopy groups.

The fundamental combinatorial structure of a net in CP 2 is its associated set of mutually orthogonal latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in CP 2 . Then we count these equivalence classes for small cases. Finally, we prove that the realization spaces of these classes in CP 2 are empty to show some non-existence results for 4-nets in CP 2 .

A subspace arrangement defined by intersections of hyperplanes of the braid arrangement can be encoded by an edge colored hypergraph. It turns out that the characteristic polynomial of this type of subspace arrangement is given by a generalized chromatic polynomial of the associated edge colored hypergraph. The main result of this paper supplies a sufficient condition for the existence of non-trivial Massey products of the subspace arrangements complex complement. This is accomplished by studying a spectral sequence associated to the Lie coalgebras of Sinha and Walter.

This paper describes The Glosten Associates' performance of stability evaluations on 16 vessels of the University-National Oceanographic Laboratory System (UNOLS) fleet. These evaluations established a consistent baseline to aid in managing mission specific weight change for each vessel to ensure the satisfaction of stability requirements. This dedicated and diligent weight management is essential for ensuring that vessels remain within a safe stability zone while not exceeding reasonable service life allowances.