Quantum Topology And Global Anomalies

This monograph is one of the very few that specializes in the study of global anomalies in quantum field theories. A discussion of various issues associated to three dimensional physics, the Chern-Simons-Witten theories widen the scope of this book. Topics discussed here comprises: the ongoing quest for three-manifolds invariant, the role of the mapping class groups in 1. the detection and cancellation of global anomalies, 2. defining three-manifolds invariant: the geometric quantization of Chern-Simons-Witten theories; deformation quantization; study of chiral and gravitational anomalies; anomalies and the Atiyah-Patodi-Singer Index theorem; exotic spheres; global anomalies both gauge and gravitational in some six and ten dimensional supergravity and superstring theories, with an additional case study of Witten SU(2) Global Gauge Anomalies. In addition, five chapters lay out the mathematical basis for a thorough use of the topics discussed mentioned above. One chapter focus on the relationship between teichm Uller spaces, moduli spaces and mapping clas groups. Another chapter is devoted to mapping class groups and arithmetic groups. Gauge theories on Riemann surfaces are studied in well over two chapters, the first one centred on the theory of bundles and the second on connections. Many readers will find this a useful book, especially theoretical physicists and mathematicians. The material presented here will be of interest to both the experts who will find complete, detailed and precise descriptions of important topics of current interest, in mathematical physics, and to students and newcomers to the field, who will appreciate the vast amount of information provided here, especially on global anomalies.