000			03224nam a22003738i 4500
001			CR9780511543142
003			UkCbUP
005			20200124160236.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2005||||enk o ||1 0|eng|d
020			_a9780511543142 (ebook)
020			_z9780521831864 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA660 _b.O87 2005
082	0	0	_a516.3/6 _222
100	1		_aOvsienko, Valentin, _eauthor.
245	1	0	_aProjective differential geometry old and new : _bfrom the Schwarzian derivative to the cohomology of diffeomorphism groups / _cV. Ovsienko, S. Tabachnikov.
246	3		_aProjective Differential Geometry Old & New
264		1	_aCambridge : _bCambridge University Press, _c2005.
300			_a1 online resource (xi, 249 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v165
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_g1. _tIntroduction -- _g2. _tThe Geometry of the projective line -- _g3. _tThe Algebra of the projective line and cohomology of Diff(S1) -- _g4. _tVertices of projective curves -- _g5. _tProjective invariants of submanifolds -- _g6. _tProjective structures on smooth manifolds -- _g7. _tMulti-dimensional Schwarzian derivatives and differential operators -- _gAppendix 1. _tFive proofs of the Sturm theorem _gAppendix 2. _tThe Language of symplectic and contact geometry -- _gAppendix 3. _tThe Language of connections -- _gAppendix 4. _tThe Language of homological algebra -- _gAppendix 5. _tRemarkable cocycles on groups of diffeomorphisms -- _gAppendix 6. _tThe Godbillon-Vey class -- _gAppendix 7. _tThe Adler-Gelfand-Dickey bracket and infinite-dimensional Poisson geometry.
520			_aIdeas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
650		0	_aProjective differential geometry.
700	1		_aTabachnikov, Serge, _eauthor.
776	0	8	_iPrint version: _z9780521831864
830		0	_aCambridge tracts in mathematics ; _v165.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543142
999			_c518053 _d518051