Index theory with applications to mathematics and physics (Q2855814)

From Publisher's description: ``This book describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics.''NEWLINENEWLINEIn order that the authors demonstrate the Atiyah-Singer index theorem in two different ways based on \(K\)-theory and the heat kernel method, they give all the background information on such diverse topics as Fredholm operators, (elliptic) pseudo-differential operators, analysis on manifolds, principal bundles and curvature, and \(K\)-theory. Many applications of the theorem are given, with emphasis on low-dimensional topology and gauge theoretic particle physics.NEWLINENEWLINEThus the book introduces various topics with basic examples and aspects in recent developments and includes many discussion sections to illuminate the thinking behind the more general theory. This monograph is informative and well written in a systematic way.