{"product_id":"lie-groupoids-and-lie-algebroids-in-differential-geometry-paperback-9780521348829","title":"Lie Groupoids and Lie Algebroids in Differential Geometry (Paperback) 9780521348829","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLie Groupoids and Lie Algebroids in Differential Geometry\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eK. Mackenzie (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521348829, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 25 June 1987\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e344 pages\u003cbr\u003e22.8 x 15.2 x 2.1 cm, 0.544 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. The algebra of groupoids\u003cbr\u003e 2. Topological groupoids\u003cbr\u003e 3. Lie groupoids and Lie algebroids\u003cbr\u003e 4. The cohomology of Lie algebroids\u003cbr\u003e 5. An obstruction to the integrability of transitive Lie algebroids\u003cbr\u003e Appendix A: On principal bundles and Atiyah sequences\u003cbr\u003e Appendix B: On Lie groups and Lie algebras\u003cbr\u003e Appendix C: On vector bundles\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\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":46007114268952,"sku":"9780521348829","price":78.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521348829i_09fb87d3-d9fc-4725-9961-46b6dd179429.jpg?v=1691375543","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lie-groupoids-and-lie-algebroids-in-differential-geometry-paperback-9780521348829","provider":"Freshly Printed Books","version":"1.0","type":"link"}