One of the best ways to learn topology is to read the classics. This translation of the 2005 Russian edition include the original methods and constructions from the originals of the 1950s and 1960s. The extended entries include Pontrjagin's article on smooth manifolds and their application in homotopy theory; Thoms' work on global properties of differential manifolds; Novikov's paper on homotropy properties of Tom complexes; papers by Smale on the generalized Poincare's conjecture in dimensions greater than four and the structure of manifolds; Quillen's article on the formal group laws of...

This volume gathers the contributions from the international conference "Intelligence of Low Dimensional Topology 2006," which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

It is not so much an absence of the right theory that has thwarted attempts by physicists to understand the natural world, contends Rosen (City U. of New York), but the unacknowledged presence of deeply ingrained assumptions about the world that are essentially incompatible with the radically non-classical phenomena underlying it. He explores what might be called the metaphysics of physics, or maybe just its geometry: as the series title might suggest, topology plays a major role in the discussion.

Provides a view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. This book covers basic notions in knot theory, as well as methods for handling open problems such as unknotting number and non-algebraic tangles.

Assisted by Scott Olsen (Central Florida Community College, USA)
This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the “Mathematics of Harmony,” a new interdisciplinary direction of modern science. This direction has its origins in “The Elements” of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized...

Based on Einstein's static universe model, this work presents technically viable alternative interpretations to all pillars of Big Bang cosmology in the context of a new 'continuous-state' cosmological paradigm able to elucidate many contemporary problems plaguing the standard model of particle physics.

This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”

This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (107).

A collection of papers on various areas of current interest in mathematical biology, such as epidemic disease modeling, including the effects of vaccination and strain replacement; immunology, such as T-Cell dynamics and the mechanism of phagocytosis; knot theory; DNA computation; and Boolean networks.

The Maxwell, Einstein, Schr dinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space...