02894nam a22003855i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003100137082001500168100003600183245011100219264004600330300003400376336002600410337002600436338003600462347002400498490004400522505029900566520128900865650001702154650003402171650001702205650002702222700002802249710003402277773002002311776003602331830004402367856009702411978-1-4020-3416-9DE-He21320260521092054.0cr nn 008mamaa100301s2005    ne |    s    |||| 0|eng d  a9781402034169  a997814020341697 a10.1007/1-4020-3416-42doi04a516.362231 aVassiliou, Efstathios.eauthor.10aGeometry of Principal Sheavesh[electronic resource] /cby Efstathios Vassiliou ; edited by M. Hazewinkel. 1aDordrecht :bSpringer Netherlands,c2005.  aXVI, 444 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aMathematics and Its Applications ;v5780 aSheaves and all that -- The category of differential triads -- Lie sheaves of groups -- Principal sheaves -- Vector and associated sheaves -- Connections on principal sheaves -- Connections on vector and associated sheaves -- Curvature -- Chern-Weil theory -- Applications and further examples.  aThe book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG. 0aMATHEMATICS. 0aGLOBAL DIFFERENTIAL GEOMETRY.14aMATHEMATICS.24aDIFFERENTIAL GEOMETRY.1 aHazewinkel, M.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781402034152 0aMathematics and Its Applications ;v57840uhttp://dx.doi.org/10.1007/1-4020-3416-4zVer el texto completo en las instalaciones del CICY