Singular Spaces

Singular Spaces
Author: Jo Farb Hernandez
Publisher: Marquand Books
Total Pages: 608
Release: 2013
Genre: Art
ISBN:

Published by leading outsider art imprint Raw Vision, Singular Spaces is a groundbreaking survey of art environments created by self-taught artists from across Spain. The book introduces and examines 45 artists and their idiosyncratic sculptures, gardens and buildings, most of which have never been published. The sites are developed organically, without formal architectural or engineering plans; they are at once evolving and complete. Often highly fanciful and quixotic, the work is frequently characterized by incongruous juxtapositions, an approach that appears impulsive and spontaneous. Director of the organization SPACES (Saving and Preserving Arts and Cultural Environments), Jo Farb Hernández, combines detailed case studies of the artists and their work with contextualized historical and theoretical references to art history, anthropology, architecture, Spanish area studies and folklore. Breaking down the standard compartmentalization of genres, she reveals how most creators of art environments, who are building within their own personal spaces, fuse their creations with their daily lives.

Differential Geometry of Singular Spaces and Reduction of Symmetry

Differential Geometry of Singular Spaces and Reduction of Symmetry
Author: J. Śniatycki
Publisher: Cambridge University Press
Total Pages: 249
Release: 2013-06-13
Genre: Mathematics
ISBN: 1107067383

In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.

Spinors on Singular Spaces and the Topology of Causal Fermion Systems

Spinors on Singular Spaces and the Topology of Causal Fermion Systems
Author: Felix Finster
Publisher: American Mathematical Soc.
Total Pages: 96
Release: 2019-06-10
Genre: Mathematics
ISBN: 1470436213

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

Topology of Singular Spaces and Constructible Sheaves

Topology of Singular Spaces and Constructible Sheaves
Author: Jörg Schürmann
Publisher: Birkhäuser
Total Pages: 461
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034880618

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.

Categorical Framework for the Study of Singular Spaces

Categorical Framework for the Study of Singular Spaces
Author: William Fulton
Publisher: American Mathematical Soc.
Total Pages: 174
Release: 1981
Genre: Categories
ISBN: 0821822438

In several areas of geometry and topology it has become apparent that the traditional covariant and contravariant functors are insufficient, particularly for dealing with geometric questions about singular spaces. We develop here a new formalism called bivariant theories. These are simultaneous generalizations of covariant group valued "homology-like" theories and contravariant ring valued "cohomology-like" theories. Most traditional pairs of covariant and contravariant theories turn out to extend to bivariant theories. A bivariant theory assigns a group not to an object but to a morphism of the original category; it has products compatible with composition of morphisms. We will also define transformations from one bivariant theory to another, called Grothendieck transformations, which generalize ordinary natural transformations. A number of standard natural transformations turn out to extend to Grothendieck transformations, and this extension has deep consequences.

Tight Spaces

Tight Spaces
Author: Kesho Scott
Publisher: Singular Lives
Total Pages: 260
Release: 1999-04
Genre: Fiction
ISBN:

This expanded edition of Tight Spaces includes six new essays that explore the fulfilling spaces inhabited by Kesho Scott, Cherry Muhanji, and Egyirba High since their book was originally published in 1987. Tight Spaces won the American Book Award in 1988.

Sur les Groupes Hyperboliques d’après Mikhael Gromov

Sur les Groupes Hyperboliques d’après Mikhael Gromov
Author: Etienne Ghys
Publisher: Springer Science & Business Media
Total Pages: 289
Release: 2013-12-11
Genre: Mathematics
ISBN: 1468491679

The theory of hyperbolic groups has its starting point in a fundamental paper by M. Gromov, published in 1987. These are finitely generated groups that share important properties with negatively curved Riemannian manifolds. This monograph is intended to be an introduction to part of Gromov's theory, giving basic definitions, some of the most important examples, various properties of hyperbolic groups, and an application to the construction of infinite torsion groups. The main theme is the relevance of geometric ideas to the understanding of finitely generated groups. In addition to chapters written by the editors, contributions by W. Ballmann, A. Haefliger, E. Salem, R. Strebel, and M. Troyanov are also included. The book will be particularly useful to researchers in combinatorial group theory, Riemannian geometry, and theoretical physics, as well as post-graduate students interested in these fields.

Analytic and Geometric Study of Stratified Spaces

Analytic and Geometric Study of Stratified Spaces
Author: Markus J. Pflaum
Publisher: Springer
Total Pages: 233
Release: 2003-07-01
Genre: Mathematics
ISBN: 3540454365

The book provides an introduction to stratification theory leading the reader up to modern research topics in the field. The first part presents the basics of stratification theory, in particular the Whitney conditions and Mather's control theory, and introduces the notion of a smooth structure. Moreover, it explains how one can use smooth structures to transfer differential geometric and analytic methods from the arena of manifolds to stratified spaces. In the second part the methods established in the first part are applied to particular classes of stratified spaces like for example orbit spaces. Then a new de Rham theory for stratified spaces is established and finally the Hochschild (co)homology theory of smooth functions on certain classes of stratified spaces is studied. The book should be accessible to readers acquainted with the basics of topology, analysis and differential geometry.

Lectures on Spaces of Nonpositive Curvature

Lectures on Spaces of Nonpositive Curvature
Author: Werner Ballmann
Publisher: Birkhäuser
Total Pages: 114
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034892403

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.