Character Map In Non Abelian Cohomology The Twisted Differential And Generalized
DOWNLOAD
Download Character Map In Non Abelian Cohomology The Twisted Differential And Generalized PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Character Map In Non Abelian Cohomology The Twisted Differential And Generalized book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Character Map In Non Abelian Cohomology The Twisted Differential And Generalized
DOWNLOAD
Author : Domenico Fiorenza
language : en
Publisher: World Scientific
Release Date : 2023-08-11
Character Map In Non Abelian Cohomology The Twisted Differential And Generalized written by Domenico Fiorenza and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with Mathematics categories.
This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.
The Character Map In Non Abelian Cohomology
DOWNLOAD
Author : Domenico Fiorenza
language : en
Publisher:
Release Date : 2023
The Character Map In Non Abelian Cohomology written by Domenico Fiorenza and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Cohomology operations categories.
Rethinking Thomas Kuhn S Legacy
DOWNLOAD
Author : Yafeng Shan
language : en
Publisher: Springer Nature
Release Date : 2024-08-09
Rethinking Thomas Kuhn S Legacy written by Yafeng Shan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-09 with Science categories.
Thomas Kuhn is widely considered as one of the most important philosophers of science in the 20th century and his The Structure of Scientific Revolutions is regarded as one of the most influential works in the philosophy of science. This book not only revisits his legacy in the history and philosophy of science but also explores and reflects on the prospect of the Kuhnian philosophy. Moreover, it includes the edited text of Kuhn’s ‘Does Knowledge Grow?’, which was never published before. Comprised of 15 newly written chapters by leading Kuhn scholars and philosophers of science across the globe from ten countries, this book is of great interest to researchers and advanced students, but also to general readers.
Homology Cohomology And Sheaf Cohomology For Algebraic Topology Algebraic Geometry And Differential Geometry
DOWNLOAD
Author : Jean H. Gallier
language : en
Publisher: World Scientific Publishing Company
Release Date : 2022
Homology Cohomology And Sheaf Cohomology For Algebraic Topology Algebraic Geometry And Differential Geometry written by Jean H. Gallier and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Algebraic topology categories.
Homology and cohomology -- De Rham cohomology -- Singular homology and cohomology -- Simplicial homology and cohomology -- Homology and cohomology of CW complexes -- Poincaré duality -- Presheaves and sheaves; Basics -- Cech cohomology with values in a presheaf -- Presheaves and sheaves; A deeper look -- Derived functors, [delta]-functors, and [del]-functors -- Universal coefficient theorems -- Cohomology of sheaves -- Alexander and Alexander-Lefschetz duality -- Spectral sequences.
Lecture Notes In Algebraic Topology
DOWNLOAD
Author : James Frederic Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lecture Notes In Algebraic Topology written by James Frederic Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic andgeometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, someknowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstructiontheory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to presentproofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, andhomological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Connections In Classical And Quantum Field Theory
DOWNLOAD
Author : Luigi Mangiarotti
language : en
Publisher: World Scientific
Release Date : 2000-04-28
Connections In Classical And Quantum Field Theory written by Luigi Mangiarotti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-28 with Science categories.
Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.
Stable Stems
DOWNLOAD
Author : Daniel C. Isaksen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Stable Stems written by Daniel C. Isaksen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-13 with Education categories.
The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, the author also resolves all hidden extensions by 2, η, and ν through the 59-stem, except for a few carefully enumerated exceptions that remain unknown. The analogous classical stable homotopy groups are easy consequences. The author also computes the motivic stable homotopy groups of the cofiber of the motivic element τ. This computation is essential for resolving hidden extensions in the Adams spectral sequence. He shows that the homotopy groups of the cofiber of τ are the same as the E2-page of the classical Adams-Novikov spectral sequence. This allows him to compute the classical Adams-Novikov spectral sequence, including differentials and hidden extensions, in a larger range than was previously known.
Mathematical Reviews
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Differential Geometry For Physicists
DOWNLOAD
Author : Bo-yu Hou
language : en
Publisher: World Scientific Publishing Company
Release Date : 1997-10-31
Differential Geometry For Physicists written by Bo-yu Hou and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-31 with Science categories.
This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
Encyclopaedia Of Mathematics
DOWNLOAD
Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.