000			03033nam a22004335i 4500
001			978-1-4020-3416-9
003			DE-He213
005			20251006084455.0
007			cr nn 008mamaa
008			100301s2005 ne | s |||| 0|eng d
020			_a9781402034169
020			_a99781402034169
024	7		_a10.1007/1-4020-3416-4 _2doi
082	0	4	_a516.36 _223
100	1		_aVassiliou, Efstathios. _eauthor.
245	1	0	_aGeometry of Principal Sheaves _h[electronic resource] / _cby Efstathios Vassiliou ; edited by M. Hazewinkel.
264		1	_aDordrecht : _bSpringer Netherlands, _c2005.
300			_aXVI, 444 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aMathematics and Its Applications ; _v578
505	0		_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.
520			_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.
650		0	_aMATHEMATICS.
650		0	_aGLOBAL DIFFERENTIAL GEOMETRY.
650	1	4	_aMATHEMATICS.
650	2	4	_aDIFFERENTIAL GEOMETRY.
700	1		_aHazewinkel, M. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781402034152
830		0	_aMathematics and Its Applications ; _v578
856	4	0	_uhttp://dx.doi.org/10.1007/1-4020-3416-4 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c60450 _d60450