Turaev, V., Universite Louis Pasteur, Strasbourg, France

Introduction to Combinatorial Torsions

Lectures in Mathematics, ETH Zurich

Approx. 144 pages. Softcover
ISBN 3-7643-6403-3
English
Due in September 200

This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on
torsions of 3-dimensional manifolds.

The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss
connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the
multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions
and the Seiberg-Witten invariant of 3-manifolds.
The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.

Chipot, M., Universitat Zurich

Elements of Nonlinear Analysis

Birkhauser Advanced Texts

Approx. 272 pages. Hardcover
ISBN 3-7643-6406-8
English
Due in October 2000

This textbook explores the vast field of nonlinear analysis by emphasizing the underlying ideas rather than the
sophisticated refinements of the theory.

Two classical examples from physics, namely elasticity and diffusion, serve to motivate the theoretical parts that are then applied to various aspects of elliptic and parabolic problems. In particular, existence,
uniqueness, regularity and approximation of solutions for quasilinear and monotone problems are studied, as well as some new aspects of the calculus of variations including Young measures or approximation of
minimizing sequences. The book is reasonably selfcontained.
Wherever possible, original proofs are given that are not to be found elsewhere. The text is geared towards graduate students and nonspecialists in nonlinear analysis who wish to become acquainted with the basic ideas of the subject. The study of this book will enable the reader to access the many ramifications of the field.

Beltita, D., Roumanian Academy, Bucharest (D.B.);
Profs. Sabac, M., University of Bucharest (M.S.)

Lie Algebras of Bounded Operators

Operator Theory: Advances and Applications vol.120

Approx. 228 pages. Hardcover
ISBN 3-7643-6404-1
Due in October 2000

There is a fruitful and fascinating interaction between infinite dimensional operator theory (particularly
decomposable, scalar and spectral generalized operator theory due to C. Foias and I. Colojoara) and Lie algebra theory.

The present book is the first devoted to this field, ranging from some short historical notes to the most recent developments. Nilpotence criteria, infinite dimensional variants of Lie's theorem for solvable
systems of bounded operators, spectral properties of elements of semisimple Lie algebras and simultaneous triangularisation are expounded.
The book is self-contained and features an extensive bibliography. It is aimed at postgraduate students and researchers who are introduced to an interesting recent area of research and will learn some new methods
useful for both of the domains ・operator theory and Lie algebra theory.

Jean-Pierre Fouque, George Papanicolaou, K. Ronnie Sircar

Derivatives in Financial Markets with Stochastic Volatility

Description
This book addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors from large trading institutions to pension funds. It presents mathematical and statistical tools that exploit the
bursty nature of market volatility. The mathematics is introduced through examples and illustrated with simulations and the modelin approach that is described is validated and tested on market data. The material is suitable for a one semester course for graduate students who have had exposure to methods of stochastic modeling and arbitrage pricing theory in finance. It is easily accessible to derivatives practitioners in the
financial engineering industry.

Chapter Contents
1. The Black-Scholes theory of derivative pricing; 2. Introduction to stochastic volatility models; 3. Scales in mean-reverting stochastic volatility; 4. Tools for estimating the rate of mean-reversion; 5. Symptotics for pricing European derivatives; 6. Implementation and stability; 7. Hedging strategies; 8. Application to exotic derivatives; 9. Application to American derivatives; 10. Generalizations; 11. Applications to interest rates
models.

Binding: Hardback
Bibliographic information:
237 x 161 mm 216pp
0.435kg
ISBN: 0521791634
Published 14 September 2000

Thomas Breuer

Characters and Automorphism Groups of Compact Riemann Surfaces

London Mathematical Society Lecture Notes Series vol.280

Description
This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as
factor groups of Fuchsian groups. The author uses modern methods from computational group theory and
representation theory, providing classifications of all automorphism groups up to genus 48. The book also
classifies the ordinary characters for several groups, arising from the action of automorphisms on the space
of holomorphic abelian differentials of a compact Reimann surface. This book is suitable for graduate
students and researchers in group theory, representation theory, complex analysis and computer algebra.


Chapter Contents
Preface; Notation; 1. Compact Riemann surfaces; 2.
Group characters; 3. Automorphisms of compact
Riemann surfaces; 4. Generation of groups; 5.
Classification for small genus; 6. Classification for fixed
group: real characters; 7. Classification for fixed group:
nonreal irrationalities; Appendix A. Abelian inariants;
Appendix B. Irreducible characters; Appendix C.
Maillet's determinant; Bibliography; Index.

Binding: Paperback
Bibliographic information:
ISBN: 0521798094
Published 21 September 2000
Not yet published -
available from September
2000