One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an...
One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than ...
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a trea...
This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and...
During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken and Poincare on the Poincare conjectures, and sketching a proof of Haken's main result.
During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing....
This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof of the cancellation of all divergences in an arbitrary interaction. The author also introduces a new method of renormalizing an arbitrary Feynman amplitude, a method that is simpler than previous approaches and can be used to study the renormalized perturbation series in quantum field theory.
This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof...
This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.
This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general settin...
This work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research.
This work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna t...
