000			03021cam a2200289 i 4500
001			136739
003			ISI Library, Kolkata
005			20160407155237.0
008			150219s2015 riu b 001 0 eng
020			_a9781470422141 (alk. paper)
040			_aISI Library _beng
082	0	4	_a510MS _223 _bAm512
100	1		_aBuchstaber, Victor M.
245	1	0	_aToric topology / _cVictor M. Buchstaber and Taras E. Panov.
260			_aProvidence : _bAmerican Mathematical Society, _c2015.
300			_axiii, 518 p. : _billustrations ; _c27 cm.
490	0		_aMathematical surveys and monographs ; _vv 204.
504			_aIncludes bibliographical references and index.
505	0		_a1. Geometry and combinatorics of polytopes -- 2. Combinatorial structures -- 3. Combinatorial algebra of face rings -- 4. Moment-angle complexes -- 5. Toric varieties and manifolds -- 6. Geometric structures on moment-angle manifolds -- 7. Half-dimensional torus actions -- 8. Homotopy theory of polyhedral products -- 9. Torus actions and complex cobordism -- Appendix A. Commutative and homological algebra -- Appendix B. Algebraic topology -- Appendix C. Categorial constructions -- Appendix D. Bordism and cobordism -- Appendix E. Formal group laws and Hirzebruch genera -- Bibliography -- Index.
520			_a"This 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. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area"--Back cover.
650		0	_aToric varieties.
650		0	_aAlgebraic varieties.
650		0	_aAlgebraic topology.
650		0	_aAlgebraic Geometry.
700	1		_aPanov, Taras E., _eauthor
942			_2ddc _cBK
999			_c420769 _d420769