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Character Map In Nonabelian Cohomology, The: Twisted, Differential, And Generalized
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Character Map In Nonabelian Cohomology, The: Twisted, Differential, And Generalized
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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.
General
Imprint: |
World Scientific Publishing Co Pte Ltd
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Country of origin: |
Singapore |
Release date: |
August 2023 |
Authors: |
Domenico Fiorenza
• Hisham Sati
• Urs Schreiber
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Pages: |
250 |
ISBN-13: |
978-981-12-7669-9 |
Categories: |
Books
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LSN: |
981-12-7669-2 |
Barcode: |
9789811276699 |
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