{"product_id":"topics-in-cyclic-theory-hardback-9781108479615","title":"Topics in Cyclic Theory (Hardback) 9781108479615","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTopics in Cyclic Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDaniel G. Quillen (Author), Gordon Blower (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108479615, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 9 July 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e328 pages, 60 exercises\u003cbr\u003e23.4 x 15.6 x 2.2 cm, 0.59 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The monograph is an excellent introduction to cyclic theory and an absolute must to any academic library, let alone a superb first-hand account and a selfless tribute to the late Daniel G. Quillen.' Igor V. Nikolaev, zbMATH\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eNoncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988–92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. Background results\u003cbr\u003e 2. Cyclic cocycles and basic operators\u003cbr\u003e 3. Algebras of operators\u003cbr\u003e 4. GNS algebra\u003cbr\u003e 5. Geometrical examples\u003cbr\u003e 6. The algebra of noncommutative differential forms\u003cbr\u003e 7. Hodge decomposition and the Karoubi operator\u003cbr\u003e 8. Connections\u003cbr\u003e 9. Cocycles for a commutative algebra over a manifold\u003cbr\u003e 10. Cyclic cochains\u003cbr\u003e 11. Cyclic cohomology\u003cbr\u003e 12. Periodic cyclic homology\u003cbr\u003e References\u003cbr\u003e List of symbols\u003cbr\u003e Index of notation\u003cbr\u003e Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical physics [\u003ca title=\"See our other books on Mathematical physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20physics%20%5BPHU%5D%22\"\u003ePHU\u003c\/a\u003e], Differential \u0026amp; Riemannian geometry [\u003ca title=\"See our other books on Differential \u0026amp; Riemannian geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Differential%20\u0026amp;%20Riemannian%20geometry%20%5BPBMP%5D%22\"\u003ePBMP\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46266359218456,"sku":"9781108479615","price":97.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781108479615i.jpg?v=1696706017","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/topics-in-cyclic-theory-hardback-9781108479615","provider":"Freshly Printed Books","version":"1.0","type":"link"}