000			02207cam a2200277 i 4500
001			18498061
005			20250610110114.0
008			150219s2015 riu b 001 0 eng
020			_a9781470422141
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB316 Q5 NBHM _qCSL
100	1		_aBuchstaber, V. M. _eauthor. _9812342
245	1	0	_aToric topology
264		1	_aProvidence : _bAmerican Mathematical Society, _c2015.
300			_axiii, 518 p. ; _c27 cm.
490	0		_aMathematical surveys and monographs ; _v204
504			_aIncludes bibliographical references (pages (495-509) and index.
520			_aThis book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism.
650		0	_aToric varieties. _9812343
650		0	_aAlgebraic varieties. _9812344
650		0	_aAlgebraic topology.
650		0	_aGeometry, Algebraic. _9812345
700	1		_aPanov, Taras E., _eco-author. _9812346
942			_2CC _n0 _cTEXL _hB316 Q5 NBHM
999			_c1431545 _d1431545