Toric Topology
Seiten
2015
American Mathematical Society (Verlag)
978-1-4704-2214-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2214-1 (ISBN)
Examines 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.
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.
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.
Victor M. Buchstaber, Steklov Mathematical Institute, Moscow, Russia. Taras E. Panov, Institute of Theoretical and Experimental Physics, Moscow, Russia.
Geometry and combinatorics of polytopes
Combinatorial structures
Combinatorial algebra of face rings Moment-angle complexes
Toric varieties and manifolds
Geometric structures on moment-angle manifolds
Half-dimensional torus actions
Homotopy theory of polyhedral products
Torus actions and complex cobordism
Commutative and homological algebra
Algebraic topology
Categorical constructions
Bordism and cobordism
Formal group laws and Hirzebruch genera
Bibliography
Index
Erscheint lt. Verlag | 30.8.2015 |
---|---|
Reihe/Serie | Mathematical Surveys and Monographs |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 1085 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 1-4704-2214-X / 147042214X |
ISBN-13 | 978-1-4704-2214-1 / 9781470422141 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
49,95 €
Buch | Hardcover (2022)
Freies Geistesleben (Verlag)
24,00 €