Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW complex in which the number of p-cells equals the p-th betti number.

A simplicial poset P (also called a boolean poset and a poset of boolean type) is a finite poset with a smallest element 0̂ such that every interval [0̂, y] for y ∈ P is a boolean algebra, i.e., [0̂, y] is isomorphic to the set of all subsets of a finite set, ordered by inclusion. The set of all faces of a (finite) simplicial complex with empty set added forms a simplicial poset ordered by inclusi...

Let Γ be a discrete group, defined by a presentation P = 〈ai | rj〉, say, or as the fundamental group of a connected CW-complex X. Remark 1.1. Let XP be the CW-complex with a single 0-cell E , one 1-cell E i for each ai (oriented accordingly), and one 2-cell E 2 j for each rj , with attaching map ∂E j → X (1) P that reads off the word rj in the generators {ai}. Then, by the Seifert–van Kampen Th...

For a simply connected rationally elliptic CW-complex X, we show that the cohomology and homotopy Euler–Poincaré characteristics are related to two new numerical invariants namely $$\eta _{X}$$ $$\rho which define using Whitehead exact sequences of Quillen Sullivan models X.

The plant cell wall (CW) compartment, or apoplast, is host to a highly dynamic proteome, comprising large numbers of both enzymatic and structural proteins. This reflects its importance as the interface between adjacent cells and the external environment, the presence of numerous extracellular metabolic and signaling pathways, and the complex nature of wall structural assembly and remodeling du...

How many two-cells must two finite CW-complexes have to admit a common, but not covering? Leighton's theorem says that both complexes two-cells. We construct an almost (?) minimal example with in each complex.

We introduce temporal tagging, a general tagging principle that takes into account when tags were generated. We use this temporal information to identify points of interest in extended recordings of complex events. We empirically demonstrate the utility of the approach in a successful user trial of a system ChattyWeb (CW) that allows students to access lecture recordings. CW coindexes students’...

It is well known that under mild conditions on a connected topological space X , connected covers of X may be classified via conjugacy classes of subgroups of the fundamental group of X . In [1], we extend these results to the study of immersions into 2-dimensional CW -complexes. An immersion f : D → C between CW -complexes is a cellular map such that each point y ∈ D has a neighborhood U that ...

Abstract The formation of Ce 2 O 3 from cerium metal requires complex reducing conditions. Alternatively, we show that different stoichiometries and structures oxides can be generated in high‐temperature laser experiments by varying the availability oxygen use either pulsed ablation (PLA) or continuous wave (CW) heating metal. X‐ray diffraction Raman spectroscopy suggest a low structural order ...