This is a study of manifold identities focusing on music and musicology.

François Laruelle proposes a theory of identity rooted in scientific notions of symmetry and chaos, emancipating thought from the philosophical paradigm of Being and reconnecting it with the real world. Unlike most contemporary philosophers, Laruelle does not believe language, history, and the world shape identity but that identity determines our relation to these phenomena. Both critical and constructivist, Theory of Identities finds fault with contemporary philosophy's reductive relation to science and its attachment to notions of singularity, difference, and multiplicity, which extends this crude approach. Laruelle's new theory of science, its objects, and philosophy, introduces an original vocabulary to elaborate the concepts of determination, fractality, and artificial philosophy, among other ideas, grounded in an understanding of the renewal of identity. Laruelle's work repairs the rift between philosophical and scientific inquiry and rehabilitates the concept of identity that continental philosophers have widely criticized. His argument positions him clearly against Deleuze, Badiou, the new materialists, and other thinkers who stray too far from empirical approaches that might revitalize philosophy's practical applications.

A fresh look at post-Soviet Russia and Eurasia and at the Soviet historical background that shaped the present.

Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar‚ duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-;Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand H”lder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

Blake's Drama challenges conventional views of William Blake's multimedia work by reinterpreting it as theatrical performance. Viewed in its dramatic contexts, this art form is shown to provoke an active spectatorship and to depict identity as paradoxically essential and constructed, revealing Blake's investments in drama, action, and the body.

Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework.An 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on.This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.Technically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings.This approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis.

Focusing on Cardiff, the capital city of Wales in the UK, this book reflects on a contemporary small European city – its development, characteristics, and present struggles. Following a century in which it was dubbed the world’s ‘coaltropolis’, the decline in demand for coal meant that Cardiff endured an acute process of de-industrialisation. In seeking to address this and the related high levels of unemployment, it has experienced a process of cultural and social reinvention since the 1980s, and more significantly after Wales turned into a devolved nation in the late 1990s. Cardiff’s development from a small port into a capital city is examined and special attention is paid to the city’s cultural and social transformation in recent decades that has relied on the expansion of specific cultural clusters and tourism, which have been decisive for the transformation of its cultural identity and in shaping the city’s individual and collective memories and identities. Cardiff epitomises a quintessential case of urban reinvention, cultural regeneration, and social transformation, lying between two apparently contradictory paradigms: the need to respond to global demands and the effort to maintain its cultural distinctiveness and Welsh roots. Therefore, it sets the scene for a wider reflection on small cities, especially in the European setting, and what generally characterises these cities: their liveability, cultural creativity and community empowerment, as well as the fact that they facilitate mobility and social interaction. These worldly cities, the book contends, present interesting opportunities and challenges at the urban, economic, social and cultural levels that rely on more human-scale, people-based approaches to cities, thus defying existing urban hierarchies and categorisations.

Geometry of Manifolds

Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout. The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.