Geometry category: 871 books

The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s–early 1970s in a complete classification...

In preparing this monograph I had three objectives. First, I wanted to introduce the reader to some topics in mathematics that seldom receive coverage in typical high school and college math programs. The topics include axioms, sets, logic, truth tables and plausible reasoning. In the sections on...

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded...

We propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied. This is a sequel of a book...

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 such as fr-codes and robot motion planning. The...

Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up...

Even Distribution and Spherical Ball-Packing is a book about the continuous uniform distribution or rectangular distribution. A family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients...

Many disciplines are concerned with manipulating geometric (or spatial) objects in the computer – such as geology, cartography, computer aided design (CAD), etc. – and each of these have developed their own data structures and techniques, often independently. Nevertheless, in many cases the object types and the spatial queries are similar, and this book attempts to find a common theme.

This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist­ ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the...

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary...

These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material...

1. On sait combien, depuis quelques années, s'est déjà montrée féconde la conception qui fait de la matière une agglomération de centres électrisés ou électrons, ceux-ci fournissant le lien nécessaire entre l'éther,...

Le 9 novembre 1919, la Société royale et la Société astronomique de Londres se réunissaient en séance solennelle, sous la présidence de Sir Joseph Thomson, pour recevoir communication des résultats obtenus par les deux expéditions chargées d’observer l’éclipse totale de Soleil du 29...