New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
 EMS Tracts in Mathematics 2010; 290 pp; hardcover Volume: 10 ISBN-10: 3-03719-086-8 ISBN-13: 978-3-03719-086-9 List Price: US$78 Member Price: US$62.40 Order Code: EMSTM/10 Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $$2$$-dimensional and $$3$$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Müger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in topological aspects of quantum field theory. Table of Contents Generalities on HQFTs Group-algebras Two-dimensional HQFTs Biangular algebras and lattice HQFTs Enumeration problems in dimension two Crossed $$G$$-categories and invariants of links Modular $$G$$-categories and HQFTs Miscellaneous algebra Appendix 1. Relative HQFTs Appendix 2. State sum invariants of 3-dimensional $$G$$-manifolds Appendix 3. Recent work on HQFTs Appendix 4. Open problems Appendix 5. On the structure of braided crossed $$G$$-categories Appendix 6. Algebraic properties of Hopf $$G$$-coalgebras Appendix 7. Invariants of 3-dimensional $$G$$-manifolds from Hopf coalgebras Bibliography Index