{"product_id":"character-map-non-abelian-cohomology-the-twisted-9789811276699-new","title":"The Character Map in Non-Abelian Cohomology: The: Twisted","description":"\u003cp\u003eThis 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 \u003cem\u003en\u003c\/em\u003e-form gauge field theories appearing in string theory and the classification of topological quantum materials.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eAlthough 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.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eDevoted 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.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn 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.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544128651554,"sku":"9789811276699-new","price":106.31,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811276699.jpg?v=1776399187","url":"https:\/\/www.albakireads.com\/products\/character-map-non-abelian-cohomology-the-twisted-9789811276699-new","provider":"AlbakiReads","version":"1.0","type":"link"}