This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully pe…
This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenome…
A. Figa Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Representations des groupes lineaires p-adiques.- G.W. Mackey: Infinite-dimensional group representations and their appl…
This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference "FOLIATIONS 2012". It contains recent materials on foliation theory which is related to differential…
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Cl…
Presents results connecting set theory with the problems of general topology, primarily giving the applications of classical set theory in general topology and not considering problems involving large numbers. This book covers questions of general t…
The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles. It thu…
The behaviour under iteration of unimodal maps of aninterval, such as the logistic map, has recently attractedconsiderable attention. It is not so widely known that asubstantial theory has by now been built up for arbitrarycontinuous maps of an inte…
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups…
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds c…
Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research…
"July 1986, volume 62, number 348 (second of 6 numbers)."
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety…
The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\De…
These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various ex…
"Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields.…
The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that po…
The featured review of the AMS describes the author's earlier work in the field of approach spaces as, 'A landmark in the history of general topology'. In this book, the author has expanded this study further and taken it in a new and exciting direc…
Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent result…
This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organ…
The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bib…
The aim of this book is to promote a fibrewise perspective, particularly in topology.
This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants i…
Confusing Textbooks? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and…
Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important…
Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation. It presents the…
In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero s…
This book considers the question of the reliability of scientific methods. One method of inquiry can be said to be more reliable than another if it eventually arrives at the truth in more possible circumstances than the other method can. Kelly begin…
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help st…
maps whose topological entropy is equal to zero (i.e., maps that have only cyeles of pe 2 riods 1,2,2 , ... ) are studied in detail and elassified. Various topological aspects of the dynamics of unimodal maps are studied in Chap ter 5. We analyze th…
This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topol…
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description…
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynam…
Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that a…
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology,…
This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological…
The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another op…
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicia…
This research monograph in the field of algebraic topology contains many thought-provoking discussions of open problems and promising research directions.
Gauss diagram invariants are isotopy invariants of oriented knots in- manifolds which are the product of a (not necessarily orientable) surface with an oriented line. The invariants are defined in a combinatorial way using knot diagrams, and they ta…
This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics s…
Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessa…
These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan…
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz,…
The French mathematician and engineer Gerard Desargues (1591-1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and archite…
The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic…
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O}{\times}$ gerbe over a genus one…