Higher Index Theory (Cambridge Studies in Advanced Mathematics)
English | 2020 | ISBN-13: 978-1108491068 | 590 Pages | PDF | 3.69 MB

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 K-theory 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