{"product_id":"geometry-of-principal-sheaves-efstathios-vassiliou-9781402034152","title":"Geometry of Principal Sheaves","description":"L' inj    enuit    m  eme d' un regard neuf (celui de la science l'est toujours) peut parfois    clairer d' un jour nouveau d' anciens probl  emes. J.Monod [77, p. 13] his book is intended as a comprehensive introduction to the theory of T principalsheaves andtheirconnections inthesettingofAbstractDi?- ential Geometry (ADG), the latter being initiated by A. Mallios'sGeometry of Vector Sheaves [62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves, thus paving the way towards a uni?ed (abstract) gauge t- ory and other potential applications to theoretical physics. We elaborate on the aforementioned brief description in the sequel. Abstract (ADG) vs. Classical Di?erential Geometry (CDG). M- ern di?erential geometry is built upon the fundamental notions of di?er- tial (smooth) manifolds and ?ber bundles, based, intheir turn, on ordinary di?erential calculus. However, the theory of smooth manifolds is inadequate to cope, for - stance, with spaces like orbifolds, spaces with corners, or other spaces with more complicated singularities. This is a rather unfortunate situation, since one cannot apply the powerful methods of di?erential geometry to them or to any spaces that do not admit an ordinary method of di?erentiation. The ix x Preface same inadequacy manifests in physics, where many geometrical models of physical phenomena are non-smooth.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Efstathios Vassiliou\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1402034156\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781402034152\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/04\/2005\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 444\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.81lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.00d","brand":"Efstathios Vassiliou","offers":[{"title":"Hardcover","offer_id":48485080727807,"sku":"9781402034152","price":109.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_cb8d3e7d-afbd-4178-982f-aac8293f252f.jpg?v=1778047774","url":"https:\/\/www.whiterainbookhouse.com\/products\/geometry-of-principal-sheaves-efstathios-vassiliou-9781402034152","provider":"WR Book House","version":"1.0","type":"link"}