In this monograph we give an exposition of some recent development in homotopy theory. It relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. It is applied to K-theory localizations, to Morava-theories, to Hopkins-Smith theory of types. The method of homotopy colimits is used heavily. It is written with an advanced graduate student in topology and research homotopy theorist in mind.

This book presents a probabilistic approach to studying the fundamental role of labor in capitalist economies and develops a non-deterministic theoretical framework for the foundations of political economy. By applying the framework to real-world data, the authors offer new insights into the dynamics of growth, wages, and accumulation in capitalist development around the globe.   The book demonstrates that a probabilistic political economy based on labor inputs enables us to describe central organizing principles in modern capitalism. Starting from a few basic assumptions, it shows that the working time of employees is the main regulating variable for determining strict numerical limits on the rate of economic growth, the range of wages, and the pace of accumulation under the present global economic system. This book will appeal to anyone interested in how the capitalist mode of production works and its inherent limitations; in particular, it will be useful to scholars and students of Marxian economics. “Emmanuel Farjoun and Moshé Machover, follow up their pathbreaking work on the application of statistical physics methods to political economy in this book with David Zachariah, in which they develop methods for making educated and structured estimates of stylized facts applicable to capitalist economies. There’s a lot for economists and anyone interested in the political economy of capitalism to learn from their reasoning on these issues, including their novel and challenging suggestion of bounds on the rates of increase of use-value productivity of labor, and on the range of variation of the wage share.� Duncan K. Foley, Leo Model Professor of Economics, New School for Social Research

This book presents a probabilistic approach to studying the fundamental role of labor in capitalist economies and develops a non-deterministic theoretical framework for the foundations of political economy. By applying the framework to real-world data, the authors offer new insights into the dynamics of growth, wages, and accumulation in capitalist development around the globe. The book demonstrates that a probabilistic political economy based on labor inputs enables us to describe central organizing principles in modern capitalism. Starting from a few basic assumptions, it shows that the working time of employees is the main regulating variable for determining strict numerical limits on the rate of economic growth, the range of wages, and the pace of accumulation under the present global economic system. This book will appeal to anyone interested in how the capitalist mode of production works and its inherent limitations; in particular, it will be useful to scholars and students of Marxian economics. "Emmanuel Farjoun and Moshe Machover, follow up their pathbreaking work on the application of statistical physics methods to political economy in this book with David Zachariah, in which they develop methods for making educated and structured estimates of stylized facts applicable to capitalist economies. There's a lot for economists and anyone interested in the political economy of capitalism to learn from their reasoning on these issues, including their novel and challenging suggestion of bounds on the rates of increase of use-value productivity of labor, and on the range of variation of the wage share." Duncan K. Foley, Leo Model Professor of Economics, New School for Social Research