This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.
This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics.
This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry.
High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1.
In this book we consider deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and we characterize axiomatically the assumptions under which such results hold.
Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics.
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130].
Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec- tures.
In this second edition, the main additions are a section devoted to surfaces with constant negative curvature, and an introduction to conformal geometry.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.
The general objective of this treatise is to give a systematic presenta- tion of some of the topological and measure-theoretical foundations of the theory of real-valued functions of several real variables, with particular emphasis upon a line of thought initiated by BANACH, GEOCZE, LEBESGUE, TONELLI, and VITALI.
The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo- topic category (IV).
The first five chapters of this book form an introductory course in piece- wise-linear topology in which no assumptions are made other than basic topological notions.
Since its very existence as a separate field within computerscience, computer graphics had to make extensive use ofnon-trivial mathematics, for example, projective geometry,solid modelling, and approximation theory.
