Topology

Point-set topology, important in itself as a research discipline, underpins a wide range of mathematical areas and is consequently taught as a component of many university mathematics degree programmes. This textbook offers an accessible, modern introduction, with a particular fo...cus on helping students to build theory for themselves.
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Since its birth in Poincare's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably - resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences -... finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entree toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an apercu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
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Features Graph Theory that takes you straight to the heart of graphs. As you study along at your own pace, this study guide shows you step by step how to solve the kind of problems you're going to find on your exams. It gives you hundreds of completely worked problems with full s...olutions.
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This volume is a successor to the title listed below. This book restricts itself to three dimensions and considers both those topics which are analogues of geometry over the complex numbers and topics arising out of the modern theory of incidence structures.

Diagram geometry lies in the interaction between group theory and geometry and is an active area of research as it provides interesting combinatorial structures in geometry and shows how these can be applied to the classification of complex groups. This book provides a survey of ...research.
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