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Algebraic Topology
Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
The Adams Spectral Sequence for Topological Modular Forms
The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres throug...
nonlinear analysis and applications
In this innovative work, 43 distinguished contributors present the latest developments together with surveys of the field. Coverage encompasses several closely related disciplines and most of the results shown in this volume are unavailable in any other source. Among the important topics addressed are applications to the theory of ordinary differential equations of generalized order, degree theoretic methods in optimal control, numerical treatment of a nonlinear problem arising in heat transfer, and applications of fixed point theorems to problems in optimization and best approximation. Encouraging interdisciplinary research to stimulate further advances, Nonlinear Analysis and Applications serves as the vital reference for mathematicians, researchers, and graduate students engaged in applied mathematics, engineering, physics, industrial science, economics, optimization, probability, medicinal and operational research, and differential equations. Additionally, it is eminently suitable for use in professional seminars.
The Scoring of Baroque Concertos
Evidence indicates that the concertos of Vivaldi, Bach, Haydn etc were performed as chamber music, not the full orchestral works commonly assumed. The concertos of Vivaldi, Bach, Handel and their contemporaries are some of the most popular, and the most frequently performed, pieces of classical music; and the assumption has always been they were full orchestral works. This book takes issue with this orthodox opinion to argue quite the reverse: that contemporaries regarded the concerto as chamber music. The author surveys the evidence, from surviving printed and manuscript performance material, from concerts throughout Europe between 1685 and 1750 (the heyday of the concerto), demonstrating that concertos were nearly always played one-to-a-part at that time. He makes a particularly close study of the scoring of the bass line, discussing the question of what instruments were most appropriate and what was used when. The late Dr RICHARD MAUNDER was Fellow of Christ's College, Cambridge.
Stable Homotopy Theory
Before I get down to the business of exposition, I'd like to offer a little motivation. I want to show that there are one or two places in homotopy theory where we strongly suspect that there is something systematic going on, but where we are not yet sure what the system is. The first question concerns the stable J-homomorphism. I recall that this is a homomorphism J: ~ (SQ) ~ ~S = ~ + (Sn), n large. r r r n It is of interest to the differential topologists. Since Bott, we know that ~ (SO) is periodic with period 8: r 6 8 r = 1 2 3 4 5 7 9· . · Z o o o z On the other hand, ~S is not known, but we can nevertheless r ask about the behavior of J. The differential topologists prove: 2 Th~~: If I' = ~ - 1, so that 'IT"r(SO) ~ 2, then J('IT"r(SO)) = 2m where m is a multiple of the denominator of ~/4k th (l\. being in the Pc Bepnoulli numher.) Conject~~: The above result is best possible, i.e. J('IT"r(SO)) = 2m where m 1s exactly this denominator. status of conJectuI'e ~ No proof in sight. Q9njecture Eo If I' = 8k or 8k + 1, so that 'IT"r(SO) = Z2' then J('IT"r(SO)) = 2 , 2 status of conjecture: Probably provable, but this is work in progl'ess.
Keyboard Instruments in Eighteenth-century Vienna
Although eighteenth-century Viennese keyboard music, especially by such composers as Haydn, Mozart, and Beethoven, is among the most popular ever written, there has been surprisingly little serious research into the instruments for which it was composed. This book fills that gap. Based on evidence from primary source material, much of it previously undiscovered or neglected, Maunder traces the history and development of the various keyboard instruments available in Vienna throughout the eighteenth century--harpsichords, clavichords, and pianos--and their use by composers and performers.
Geometry, Spectral Theory, Groups, and Dynamics
This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952-2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and number theory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szegos theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate students and researchers interested in various aspects of geometry and global analysis.
On the Inductive Philosophy
Reprint of the original.
Secondary Cohomology Operations
Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS now fills that gap with the publication of the present volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among manyapplications considered are the Hopf invariant one theorem (for all primes $p$, including $p = 2$), Browder's theorem on higher Bockstein operations, and cohomology theory of Massey-Peterson fibrations. Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary ofmore advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations. The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.
