000 | 02457nam a2200361 i 4500 | ||
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001 | CR9781009091251 | ||
003 | UkCbUP | ||
005 | 20240508141513.0 | ||
006 | m|||||o||d|||||||| | ||
007 | cr|||||||||||| | ||
008 | 210426s2023||||enk o ||1 0|eng|d | ||
020 | _a9781009091251 (ebook) | ||
020 | _z9781316514887 (hardback) | ||
040 |
_aUkCbUP _beng _erda _cUkCbUP |
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050 | 0 | 0 |
_aQA613.6 _b.S36 2023 |
082 | 0 | 0 |
_a514/.72 _223/eng20220910 |
100 | 1 |
_aSchmeding, A., _eauthor. |
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245 | 1 | 3 |
_aAn introduction to infinite-dimensional differential geometry / _cAlexander Schmeding. |
264 | 1 |
_aCambridge, United Kingdom ; New York, NY : _bCambridge University Press, _c2023. |
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300 |
_a1 online resource (xiv, 267 pages) : _bdigital, PDF file(s). |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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490 | 1 |
_aCambridge studies in advanced mathematics ; _v202 |
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506 | 0 |
_aOpen Access. _fUnrestricted online access _2star |
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500 | _aTitle from publisher's bibliographic system (viewed on 12 Dec 2022). | ||
520 | _aIntroducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core. | ||
650 | 0 | _aInfinite-dimensional manifolds. | |
650 | 0 | _aGeometry, Differential. | |
776 | 0 | 8 |
_iPrint version: _z9781316514887 |
830 | 0 |
_aCambridge studies in advanced mathematics ; _v202. |
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856 | 4 | 0 | _uhttps://doi.org/10.1017/9781009091251 |
999 |
_c38413 _d38413 |