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Breadth in Contemporary Topology
This volume contains the proceedings of the 2017 Georgia International Topology Conference, held from May 22–June 2, 2017, at the University of Georgia, Athens, Georgia. The papers contained in this volume cover topics ranging from symplectic topology to classical knot theory to topology of 3- and 4-dimensional manifolds to geometric group theory. Several papers focus on open problems, while other papers present new and insightful proofs of classical results. Taken as a whole, this volume captures the spirit of the conference, both in terms of public lectures and informal conversations, and presents a sampling of some of the great new ideas generated in topology over the preceding eight years.
Modernism and the Spiritual in Russian Art
In 1911 Vasily Kandinsky published the first edition of ‘On the Spiritual in Art’, a landmark modernist treatise in which he sought to reframe the meaning of art and the true role of the artist. For many artists of late Imperial Russia – a culture deeply influenced by the regime’s adoption of Byzantine Orthodoxy centuries before – questions of religion and spirituality were of paramount importance. As artists and the wider art community experimented with new ideas and interpretations at the dawn of the twentieth century, their relationship with ‘the spiritual’ – broadly defined – was inextricably linked to their roles as pioneers of modernism. This diverse collection of ess...
Topology, Ergodic Theory, Real Algebraic Geometry
This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.
Algebraic Functions
This is a translation of Iwasawa's 1973 book, Theory of Algebraic Functions originally published in Japanese. Because the book treats mainly the classical part of the theory of algebraic functions, emphasizing analytic methods, it provides an excellent introduction to the subject from the classical viewpoint. Directed at graduate students, the book requires some basic knowledge of algebra, topology, and functions of a complex variable.
Algebraic Geometry
Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings, and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting thenecessary background along the way. Originally published in Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes andalgebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces.
Groups, Generators, Syzygies, and Orbits in Invariant Theory
The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
Hayes' Principles and Methods of Toxicology, Sixth Edition
Hayes’ Principles and Methods of Toxicology has long been established as a reliable reference to the concepts, methodologies, and assessments integral to toxicology. The new sixth edition has been revised and updated while maintaining the same high standards that have made this volume a benchmark resource in the field. With new authors and new chapters that address the advances and developments since the fifth edition, the book presents everything toxicologists and students need to know to understand hazards and mechanisms of toxicity, enabling them to better assess risk. The book begins with the four basic principles of toxicology—dose matters, people differ, everything transforms, and ...
Genomics of Plant Genetic Resources
Our lives and well being intimately depend on the exploitation of the plant genetic resources available to our breeding programs. Therefore, more extensive exploration and effective exploitation of plant genetic resources are essential prerequisites for the release of improved cultivars. Accordingly, the remarkable progress in genomics approaches and more recently in sequencing and bioinformatics offers unprecedented opportunities for mining germplasm collections, mapping and cloning loci of interest, identifying novel alleles and deploying them for breeding purposes. This book collects 48 highly interdisciplinary articles describing how genomics improves our capacity to characterize and harness natural and artificially induced variation in order to boost crop productivity and provide consumers with high-quality food. This book will be an invaluable reference for all those interested in managing, mining and harnessing the genetic richness of plant genetic resources.
Functions on Manifolds: Algebraic and Topological Aspects
This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on non-simply-connected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed.
