Elements of noncommutative geometry
Gracia Bondía, José M.
Elements of noncommutative geometry - New York: Springer, 2001. - xvi, 685 p.; pb; 24 cm. - Birkhäuser advanced texts. .
Includes bibliographical references (p. [641]-666) and indexes.
The subject of this text is an algebraic and operatorial reworking of geometry, which traces its roots to quantum physics; Connes has shown that noncommutative geometry keeps all essential features of the metric geometry of manifolds. Many singular spaces that emerge from advances in mathematics or are used by physicists to understand the natural world are thereby brought into the realm of geometry." "This book is an introduction to the language and techniques of noncommutative geometry at a level suitable for graduate students, and also provides sufficient detail to be useful to physicists and mathematicians wishing to enter this rapidly growing field. It may also serve as a reference text on several topics that are relevant to noncommutative geometry.
9781461265696
Mathematics
Geometry
Topology
Noncommutative Topology
Vector Bundles
K-theory
Linear Algebra
Spin Representation
Noncommutative Integral
Differential Calculi
Commutative Geometries
Spectral Triples
Manifold Theorem
Quantum Theory
516.3 / GRA
Elements of noncommutative geometry - New York: Springer, 2001. - xvi, 685 p.; pb; 24 cm. - Birkhäuser advanced texts. .
Includes bibliographical references (p. [641]-666) and indexes.
The subject of this text is an algebraic and operatorial reworking of geometry, which traces its roots to quantum physics; Connes has shown that noncommutative geometry keeps all essential features of the metric geometry of manifolds. Many singular spaces that emerge from advances in mathematics or are used by physicists to understand the natural world are thereby brought into the realm of geometry." "This book is an introduction to the language and techniques of noncommutative geometry at a level suitable for graduate students, and also provides sufficient detail to be useful to physicists and mathematicians wishing to enter this rapidly growing field. It may also serve as a reference text on several topics that are relevant to noncommutative geometry.
9781461265696
Mathematics
Geometry
Topology
Noncommutative Topology
Vector Bundles
K-theory
Linear Algebra
Spin Representation
Noncommutative Integral
Differential Calculi
Commutative Geometries
Spectral Triples
Manifold Theorem
Quantum Theory
516.3 / GRA
