This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Moebius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced.In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. 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.

The standoff at Cliven Bundy's ranch, the rise of white identity activists on college campuses, and the viral growth of white nationalist videos on YouTube vividly illustrate the resurgence of white supremacy and overt racism in the United States. White resistance to racial equality can be subtle as well-like art museums that enforce their boundaries as elite white spaces, "right on crime" policies that impose new modes of surveillance and punishment for people of color, and environmental groups whose work reinforces settler colonial norms. In this incisive volume, twenty-four leading sociologists assess contemporary shifts in white attitudes about racial justice in the US. Using case studies, they investigate the entrenchment of white privilege in institutions, new twists in anti-equality ideologies, and "whitelash" in the actions of social movements. Their examinations of new manifestations of racist aggression help make sense of the larger forces that underpin enduring racial inequalities and how they reinvent themselves for each new generation.

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Moebius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced.In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. 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.

Affirmative action in US college admissions has inspired fierce debate as well as several US Supreme Court cases. In this significant study, leading US professors J. Scott Carter and Cameron D. Lippard provide an in-depth examination of the issue using sociological, policy and legal perspectives to frame both pro- and anti-affirmative action arguments, within past and present Supreme Court cases. With affirmative action policy under constant attack, this is a crucial book that not only explains the state of this policy but also further deconstructs the state of race and racism in American society today.

Affirmative action in US college admissions has inspired fierce debate as well as several US Supreme Court cases. In this significant study, leading US professors J. Scott Carter and Cameron D. Lippard provide an in-depth examination of the issue using sociological, policy and legal perspectives to frame both pro- and anti-affirmative action arguments, within past and present Supreme Court cases. With affirmative action policy under constant attack, this is a crucial book that not only explains the state of this policy but also further deconstructs the state of race and racism in American society today.

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.

The standoff at Cliven Bundy's ranch, the rise of white identity activists on college campuses, and the viral growth of white nationalist videos on YouTube vividly illustrate the resurgence of white supremacy and overt racism in the United States. White resistance to racial equality can be subtle as well-like art museums that enforce their boundaries as elite white spaces, "right on crime" policies that impose new modes of surveillance and punishment for people of color, and environmental groups whose work reinforces settler colonial norms. In this incisive volume, twenty-four leading sociologists assess contemporary shifts in white attitudes about racial justice in the US. Using case studies, they investigate the entrenchment of white privilege in institutions, new twists in anti-equality ideologies, and "whitelash" in the actions of social movements. Their examinations of new manifestations of racist aggression help make sense of the larger forces that underpin enduring racial inequalities and how they reinvent themselves for each new generation.

Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of "sl(2), " both classical and quantum. Covering representations of "U(sl(2)), " quantum "sl(2), " the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals.

The classic subject of representations of "U(sl(2))" is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6"j"-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group "Ub-3.0 qb0(sl(2))" develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter "q" is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.

Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law $x(yz)=(xy)z$. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29-August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.