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Synthetic geometry of manifolds /

Kock, Anders.

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Synthetic geometry of manifolds /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Synthetic geometry of manifolds // Anders Kock.
作者:	Kock, Anders.
出版者:	Cambridge :Cambridge University Press, : c2010.,
面頁冊數:	xiii, 302 p. :ill. ;24 cm.
標題:	Geometry, Differential. -
電子資源:	http://assets.cambridge.org/97805211/16732/cover/9780521116732.jpg
ISBN:	9780521116732 :

Synthetic geometry of manifolds /
Kock, Anders.

Synthetic geometry of manifolds /Anders Kock. - Cambridge :Cambridge University Press,c2010. - xiii, 302 p. :ill. ;24 cm. - Cambridge tracts in mathematics ;180.

Includes bibliographical references (p. 293-297) and index.

"This 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 neighborhoods 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"--Provided by publisher.

ISBN: 9780521116732 :US80.00

LCCN: 2009038164Subjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641 / .K735 2010

Dewey Class. No.: 516.3/62

Synthetic geometry of manifolds /
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245 1 0 $a Synthetic geometry of manifolds / $c Anders Kock.
260 $a Cambridge : $b Cambridge University Press, $c c2010.
300 $a xiii, 302 p. : $b ill. ; $c 24 cm.
490 0 $a Cambridge tracts in mathematics ; $v 180
504 $a Includes bibliographical references (p. 293-297) and index.
520 $a "This 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 neighborhoods 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"--Provided by publisher.
520 $a "This book deals with a certain aspect of the theory of smoothmanifolds, namely (for each k) the kth neigbourhood of the diagonal. A part of the theory presented here also applies in algebraic geometry (smooth schemes). The neighbourhoods of the diagonal are classical mathematical objects. In the context of algebraic geometry, they were introduced by the Grothendieck school in the early 1960s; the Grothendieck ideas were imported into the context of smooth manifolds by Malgrange, Kumpera and Spencer, and others. Kumpera and Spencer call them "prolongation spaces of order k". The study of these spaces has previously been forced to be rather technical, because the prolongation spaces are not themselves manifolds, but live in a wider category of "spaces", which has to be described. For the case of algebraic geometry, one passes from the category of varieties to the wider category of schemes; for the smooth case, Malgrange, Kumpera and Spencer, and others described a category of "generalized differentiablemanifolds with nilpotent elements" (Kumpera and Spencer, 1973, p. 54)"--Provided by publisher.
650 0 $a Geometry, Differential. $3 523835
650 0 $a Manifolds (Mathematics) $3 612607
856 4 2 $3 Cover image $u http://assets.cambridge.org/97805211/16732/cover/9780521116732.jpg