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Author : Daniel G. Quillen
Release : 2020-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 618/5 ( reviews)
Book Synopsis Topics in Cyclic Theory by : Daniel G. Quillen
Download or read book Topics in Cyclic Theory written by Daniel G. Quillen. This book was released on 2020-07-09. Available in PDF, EPUB and Kindle. Book excerpt: This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.
Author : Daniel G. Quillen
Release : 2020-06-30
Genre : Mathematics
Kind : eBook
Book Rating : 444/5 ( reviews)
Book Synopsis Topics in Cyclic Theory by : Daniel G. Quillen
Download or read book Topics in Cyclic Theory written by Daniel G. Quillen. This book was released on 2020-06-30. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988-92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.
Author : Roger Penrose
Release : 2011-09-06
Genre : Science
Kind : eBook
Book Rating : 745/5 ( reviews)
Book Synopsis Cycles of Time by : Roger Penrose
Download or read book Cycles of Time written by Roger Penrose. This book was released on 2011-09-06. Available in PDF, EPUB and Kindle. Book excerpt: From Nobel prize-winner Roger Penrose, this groundbreaking book is for anyone "who is interested in the world, how it works, and how it got here" (New York Journal of Books). Penrose presents a new perspective on three of cosmology’s essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us? He shows how the expected fate of our ever-accelerating and expanding universe—heat death or ultimate entropy—can actually be reinterpreted as the conditions that will begin a new “Big Bang.” He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, Cycles of Time is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.
Author : Stephen J. Puetz
Release : 2011
Genre : Science
Kind : eBook
Book Rating : 330/5 ( reviews)
Book Synopsis Universal Cycle Theory by : Stephen J. Puetz
Download or read book Universal Cycle Theory written by Stephen J. Puetz. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: These simple statements hold huge implications about how the universe must operate if it was truly infinite rather than finite, as is commonly thought. In one sense, this book, Universal Cycle Theory, may seem radical because it postulates that the universe operates in ways that are dramatically different from what we are taught. Yet, this new theory is conventional in the sense that it closely conforms to virtually all existing laws, equations, and observations. There are only two elements that make the Universal Cycle Theory radical cycles and infinity. Other than that, much of what you read in this book will seem familiar and conventional. Cycles are crucial because they are reflections of how matter behaves in an infinite universe: as vortices and waves. A vortex forms when matter rotates, producing circular cycles. A wave forms when colliding matter compresses and decompresses, producing linear cycles. Infinity is crucial because it explains the extent and structure of the universe. We assume that matter is infinitely divisible in the microscopic direction and infinitely integrable in the macroscopic direction. We assume that time was infinite in the past and will be infinite in the future. This concept of infinity is unique, having never been employed in a model of the universe before. It resolves many of the paradoxes and contradictions currently riddling physics and cosmology.
Author : Joachim Cuntz
Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 448/5 ( reviews)
Book Synopsis Cyclic Homology in Non-Commutative Geometry by : Joachim Cuntz
Download or read book Cyclic Homology in Non-Commutative Geometry written by Joachim Cuntz. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
