Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized

Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized
Author :
Publisher : World Scientific
Total Pages : 248
Release :
ISBN-10 : 9789811276712
ISBN-13 : 9811276714
Rating : 4/5 (714 Downloads)

Book Synopsis Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized by : Domenico Fiorenza

Download or read book Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized written by Domenico Fiorenza and published by World Scientific. This book was released on 2023-08-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized Related Books

Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized
Language: en
Pages: 248
Authors: Domenico Fiorenza
Categories: Mathematics
Type: BOOK - Published: 2023-08-11 - Publisher: World Scientific

DOWNLOAD EBOOK

This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further gener
The Character Map in Non-abelian Cohomology
Language: en
Pages: 0
Authors: Domenico Fiorenza
Categories: Cohomology operations
Type: BOOK - Published: 2023-08-11 - Publisher: World Scientific Publishing Company

DOWNLOAD EBOOK

"Presents a novel development in fundamental aspects of algebraic topology and mathematical physics: existing "extra-ordinary" and further generalized Cohomolog
Rethinking Thomas Kuhn’s Legacy
Language: en
Pages: 341
Authors: Yafeng Shan
Categories:
Type: BOOK - Published: - Publisher: Springer Nature

DOWNLOAD EBOOK

Lecture Notes in Algebraic Topology
Language: en
Pages: 385
Authors: James F. Davis
Categories: Mathematics
Type: BOOK - Published: 2023-05-22 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies,
Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory
Language: en
Pages: 177
Authors: Ulrich Bunke
Categories: Education
Type: BOOK - Published: 2021-06-21 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a