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The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
“If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the ...
Summarizes the science of climate change and impacts on the United States, for the public and policymakers.
This report provides a comprehensive assessment of the economic consequences of outdoor air pollution in the coming decades, focusing on the impacts on mortality, morbidity, and changes in crop yields as caused by high concentrations of pollutants.
The Hamito-Semitic Etymological Dictionary, a project in the making since 1986, is the first dictionary to reflect the vocabulary of the extinct Proto-Hamito-Semitic (Proto-Afro-Asiatic) language. Reconstructed on the basis of Semitic, Ancient Egyptian, Berber, Chadic and Cushitic linguistic groups, the Dictionary plays an indispensable role in further research into the field of historical linguistics. It surpasses by far the only comparable work to date, M. Cohen's Essai comparatif sur le vocabulaire et la phonetique du chamito-semitique, published in 1947, which contains much less material and is now outdated. The Dictionary comprises more than 2,500 lexical items and includes an introduction providing valuable information on the historical phonology of Hamito-Semitic as well as an index of meanings, which supplies linguistics, archaeologists and scholars of ancient history with added insight into the culture of the ancient speakers of Proto-Hamito-Semitic. An invaluable contribution to the field of Afro-Asiatic Studies, The Hamito-Semitic Etymological Dictionary will be used and discussed by scholars for years to come.