A. J. Berrick

Bio: A. J. Berrick is an academic researcher from National University of Singapore. The author has contributed to research in topics: Conjecture & Homotopy. The author has an hindex of 15, co-authored 65 publications receiving 728 citations. Previous affiliations of A. J. Berrick include Yale-NUS College & Yale University.

Configurations, braids, and homotopy groups

Abstract: The main results of this article are certain connections between braid groups and the homotopy groups of the 2-sphere. The connections are given in terms of Brunnian braids over the disk and over the 2-sphere. The techniques arise from the natural structure of simplicial and ∆-structures on fundamental groups of configuration spaces.

An introduction to rings and modules with K-theory in view

Abstract: This book, first published in 2000, is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups About 200 exercises complement the text and introduce further topics This book provides the background material for the authors' companion volume Categories and Modules, soon to appear Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory

The tobacco-free generation proposal

Abstract: The tobacco-free generation proposal advocates legislation precluding the sale and supply of tobacco to individuals born after a certain year. The measure is aimed at overcoming defects with current youth access laws that suffer from rite-of-passage and mixed signalling effects. Since its introduction in 2010, the proposal has attracted international attention, highlighting a number of matters that the present short article discusses. Efficacy issues, including retailer compliance, supply by surrogates and illicit sales, are addressed in the broader setting of community adherence to legislation. Encouragement for the likelihood of successful implementation is provided by historical precedents. In principle objections, relating to choice and generational fairness, are considered against the criteria of consistency and proportionality. It is concluded that the measure's emphasis on the welfare of future generations and its regard for the interests of existing stakeholders provide a feasible opportunity for the ultimate eradication of tobacco supply in appropriate jurisdictions.

From acyclic groups to the Bass conjecture for amenable groups

Abstract: We prove that the Bost Conjecture on the � 1 -assembly map for countable discrete groups implies the Bass Conjecture It follows that all amenable groups satisfy the Bass Con- jecture

Composition methods in homotopy groups of spheres

Abstract: The description for this book, Compositional Methods in Homotopy Groups of Spheres. (AM-49), will be forthcoming.

The K-Book: An Introduction to Algebraic K-theory

Abstract: Projective modules and vector bundles The Grothendieck group $K_0$ $K_1$ and $K_2$ of a ring Definitions of higher $K$-theory The fundamental theorems of higher $K$-theory The higher $K$-theory of fields Nomenclature Bibliography Index