The Character Map In Non Abelian Cohomology
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Character Map In Non Abelian Cohomology The Twisted Differential And Generalized
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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
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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
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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.
Geometry Topology And Dynamics Of Character Varieties
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Author : William Mark Goldman
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Topology And Dynamics Of Character Varieties written by William Mark Goldman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.
Geometry And Physics Volume 2
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Author : Jørgen Ellegaard Andersen
language : en
Publisher: Oxford University Press
Release Date : 2018-10-18
Geometry And Physics Volume 2 written by Jørgen Ellegaard Andersen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Mathematics categories.
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
Geometry And Physics
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Author : Jørgen Ellegaard Andersen
language : en
Publisher:
Release Date : 2018
Geometry And Physics written by Jørgen Ellegaard Andersen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.
Witten Non Abelian Localization For Equivariant K Theory And The Q R 0 Theorem
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Author : Paul-Emile Paradan
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02
Witten Non Abelian Localization For Equivariant K Theory And The Q R 0 Theorem written by Paul-Emile Paradan 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 2019-12-02 with Education categories.
The purpose of the present memoir is two-fold. First, the authors obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, the authors deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, the authors use this general approach to reprove the [Q,R]=0 [Q,R]=0 theorem of Meinrenken-Sjamaar in the Hamiltonian case and obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of general spin c spinc Dirac operators.
Encyclopaedia Of Mathematics
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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.
Non Abelian Fundamental Groups And Iwasawa Theory
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Author : John Coates
language : en
Publisher: Cambridge University Press
Release Date : 2011-12-15
Non Abelian Fundamental Groups And Iwasawa Theory written by John Coates and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-15 with Mathematics categories.
This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1994-10
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10 with categories.