000 02457nam a2200361 i 4500
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
050 0 0 _aQA613.6
_b.S36 2023
082 0 0 _a514/.72
_223/eng20220910
100 1 _aSchmeding, A.,
_eauthor.
245 1 3 _aAn introduction to infinite-dimensional differential geometry /
_cAlexander Schmeding.
264 1 _aCambridge, United Kingdom ; New York, NY :
_bCambridge University Press,
_c2023.
300 _a1 online resource (xiv, 267 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v202
506 0 _aOpen Access.
_fUnrestricted online access
_2star
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.
856 4 0 _uhttps://doi.org/10.1017/9781009091251
999 _c38413
_d38413