000 02509nam a22003618i 4500
001 CR9780511691690
003 UkCbUP
005 20200124160238.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 100219s2010||||enk o ||1 0|eng|d
020 _a9780511691690 (ebook)
020 _z9780521116732 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA641
_b.K735 2010
082 0 0 _a516.3/62
_222
100 1 _aKock, Anders,
_eauthor.
245 1 0 _aSynthetic geometry of manifolds /
_cAnders Kock.
264 1 _aCambridge :
_bCambridge University Press,
_c2010.
300 _a1 online resource (xiii, 302 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v180
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _a1. Calculus and linear algebra -- 2. Geometry of the neighbour relation -- 3. Combinatorial differential forms -- 4. The tangent bundle -- 5. Groupoids -- 6. Lie theory; non-abelian covariant derivative -- 7. Jets and differential operators -- 8. Metric notions.
520 _aThis elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
650 0 _aGeometry, Differential.
650 0 _aManifolds (Mathematics)
776 0 8 _iPrint version:
_z9780521116732
830 0 _aCambridge tracts in mathematics ;
_v180.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511691690
999 _c518267
_d518265