Higher index theory
Willett, Rufus
Higher index theory - Cambridge: Cambridge University Press, 2020. - xi, 581 p. : ill. ; hb. ; 24 cm. - Cambridge studies in advanced mathematics ; 189 .
Includes bibliographical references and index.
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the Ktheory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
9781108491068
C*-algebras
Index theory (Mathematics)
K-theory
Algebra
Mathematics
512.556 / WIL
Higher index theory - Cambridge: Cambridge University Press, 2020. - xi, 581 p. : ill. ; hb. ; 24 cm. - Cambridge studies in advanced mathematics ; 189 .
Includes bibliographical references and index.
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the Ktheory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
9781108491068
C*-algebras
Index theory (Mathematics)
K-theory
Algebra
Mathematics
512.556 / WIL
