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Affirmative action in college admissions has been a polarizing policy since its inception, decried by some as unfairly biased and supported by others as a necessary corrective to institutionalized inequality. In recent years, the protected status of affirmative action has become uncertain, as legal challenges chip away at its foundations. This book looks through a sociological lens at both the history of affirmative action and its increasingly tenuous future. J. Scott Carter and Cameron D. Lippard first survey how and why so-called "colorblind" rhetoric was originally used to frame affirmative action and promote a political ideology. The authors then provide detailed examinations of a host of recent Supreme Court cases that have sought to threaten or undermine it. Carter and Lippard analyze why the arguments of these challengers have successfully influenced widespread changes in attitude toward affirmative action, concluding that the discourse and arguments over these policies are yet more unfortunate manifestations of the quest to preserve the racial status quo in the United States.
This book discusses knotted surfaces in 4-dimensional space and surveys many of the known results, including knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory.
1. A sphere -- 2. Surfaces, folds, and cusps -- 3. The inside and outside -- 4. Dimensions -- 5. Immersed surfaces -- 6. Movies -- 7. Movie moves -- 8. Taxonomic summary -- 9. How not to turn the sphere inside-out -- 10. A physical metaphor -- 11. Sarah's thesis -- 12. The eversion -- 13. The double point and fold surfaces
This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.
This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.
In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third ch...
In this “fast-paced adventure filled with thoughtful life lessons” (School Library Journal), becoming a real boy is just the beginning. Since he changed, Pino has struggled to live a quiet life with his father Gepetto. But a boy who used to be a wooden puppet doesn’t fit in well with the other villagers. When Pino creates a replica of Gepetto’s late wife and brings it to life, the two are chased out of their village by an angry mob demanding the resurrection of their own loved ones. On the run with a dying Gepetto, Pino must face a world that would seek to use—and misuse—him for his powers. And when Pino discovers that his abilities are slowly transforming him back into a puppet, he faces a choice: strike a deal with those who only want to use him, or stand up for who he really is.
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.