Differential Topology And Quantum Field Theory / Charles Nash.

Preface
Chapter I: A topological Preliminary
Chapter II: Elliptic Operators
Chapter III: Cohomology of Sheaves and Bundles
Chapter IV: Index Theory for Elliptic Operators
Chapter V: Some Algebraic Geometry
Chapter VI: Infinite Dimensional Groups
Chapter VII: Morse Theory
Chapter VIII: Instantons and Monopoles
Chapter IX: The Elliptic Geometry of Strings
Chapter X: Anomalies
Chapter XI: Conformal Quantum Field Theories
Chapter XII: Topological Field Theories
References
Index

The remarkable developments in differentials topology and how these recent adventures have been applied as a primary research tool on quantum field theory are presented in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following on from the previous work (Nash/Sen: Differential Topology for Physicist, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer Index Theory, Morse Theory, Instantons and monopoles, topological quantum field theory, string theory and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first tiem.