Fat manifolds and linear connections:
The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to this subject was proposed by Ch. Ehresmann 60 years...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2009
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| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to this subject was proposed by Ch. Ehresmann 60 years ago, attracting first mathematicians and later physicists by its transparent geometrical simplicity. Unfortunately, it does not extend well to a number of recently emerged situations of significant importance (singularities, supermanifolds, infinite jets and secondary calculus, etc.). Moreover, it does not help in understanding the structure of calculus naturally related with a connection. In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a "fat manifold" introduced here then allows the reader to build a well-working analogy of this "connection calculus" with the usual one |
| Beschreibung: | xii, 297 p. ill |
| ISBN: | 9789812819055 |
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| 520 | |a The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to this subject was proposed by Ch. Ehresmann 60 years ago, attracting first mathematicians and later physicists by its transparent geometrical simplicity. Unfortunately, it does not extend well to a number of recently emerged situations of significant importance (singularities, supermanifolds, infinite jets and secondary calculus, etc.). Moreover, it does not help in understanding the structure of calculus naturally related with a connection. In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a "fat manifold" introduced here then allows the reader to build a well-working analogy of this "connection calculus" with the usual one | ||
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| author | De Paris, Alessandro |
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| format | Electronic eBook |
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| id | DE-604.BV044636692 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:49Z |
| institution | BVB |
| isbn | 9789812819055 |
| language | English |
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| oclc_num | 1012646314 |
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| physical | xii, 297 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific Pub. Co. |
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| spelling | De Paris, Alessandro Verfasser aut Fat manifolds and linear connections Alessandro De Paris, Alexandre Vinogradov Singapore World Scientific Pub. Co. c2009 xii, 297 p. ill txt rdacontent c rdamedia cr rdacarrier The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media). The now-standard approach to this subject was proposed by Ch. Ehresmann 60 years ago, attracting first mathematicians and later physicists by its transparent geometrical simplicity. Unfortunately, it does not extend well to a number of recently emerged situations of significant importance (singularities, supermanifolds, infinite jets and secondary calculus, etc.). Moreover, it does not help in understanding the structure of calculus naturally related with a connection. In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a "fat manifold" introduced here then allows the reader to build a well-working analogy of this "connection calculus" with the usual one Differential calculus Commutative algebra Manifolds (Mathematics) Algebras, Linear Vinogradov, A. M. Sonstige oth Erscheint auch als Druck-Ausgabe 9789812819048 Erscheint auch als Druck-Ausgabe 9812819045 http://www.worldscientific.com/worldscibooks/10.1142/6904#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | De Paris, Alessandro Fat manifolds and linear connections Differential calculus Commutative algebra Manifolds (Mathematics) Algebras, Linear |
| title | Fat manifolds and linear connections |
| title_auth | Fat manifolds and linear connections |
| title_exact_search | Fat manifolds and linear connections |
| title_full | Fat manifolds and linear connections Alessandro De Paris, Alexandre Vinogradov |
| title_fullStr | Fat manifolds and linear connections Alessandro De Paris, Alexandre Vinogradov |
| title_full_unstemmed | Fat manifolds and linear connections Alessandro De Paris, Alexandre Vinogradov |
| title_short | Fat manifolds and linear connections |
| title_sort | fat manifolds and linear connections |
| topic | Differential calculus Commutative algebra Manifolds (Mathematics) Algebras, Linear |
| topic_facet | Differential calculus Commutative algebra Manifolds (Mathematics) Algebras, Linear |
| url | http://www.worldscientific.com/worldscibooks/10.1142/6904#t=toc |
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