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A Course in Homological Algebra
In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concept...
Homology Theory
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Kenelm Chillingly
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An Introduction to Homotopy Theory
Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cell-complexes and their application to homotopy groups of complexes.
Homology Theory
This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.
The Psychology of Counterfactual Thinking
This book provides a critical overview of significant developments in research and theory on counterfactual thinking that have emerged in recent years and spotlights exciting new directions for future research in this area. Key issues considered include the relations between counterfactual and casual reasoning, the functional bases of counterfactual thinking, the role of counterfactual thinking in the experience of emotion and the importance of counterfactual thinking in the context of crime and justice.
The Essays of Elia
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General Cohomology Theory and K-Theory
These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.
Wildlife in a Changing World
"Wildlife in a Changing World" presents an analysis of the 2008 IUCN Red List of Threatened Species. Beginning with an explanation of the IUCN Red List as a key conservation tool, it goes on to discuss the state of the world s species and provides the latest information on the patterns of species facing extinction in some of the most important ecosystems in the world, highlighting the reasons behind their declining status. Areas of focus in the report include: freshwater biodiversity, the status of the world s marine species, species susceptibility to climate change impacts, the Mediterranean biodiversity hot spot, and broadening the coverage of biodiversity assessments."
