zbMATH — the first resource for mathematics

Quantum invariants of knots and 3-manifolds. 3rd edition. (English) Zbl 1346.57002
de Gruyter Studies in Mathematics 18. Berlin: Walter de Gruyter (ISBN 978-3-11-044266-3/hbk; 978-3-11-043522-1/ebook). xii, 596 p. (2016).
Apart from a few new prefatory comments, this third edition of the author’s classic 1994 monograph just updates its comprehensive bibliography with references to post-2009 work of the author, Alagic, Alexandrov, Anderson, Beliakova, Bunting, Cai, Carfora, Chen, Costantino, Fuchs, Funar, Geer, Geiller, Gelea, Gilmer, Koda, Koenig, Marathe, Marche, Martelli, Ng, Okazaki, Rose, Staic, Tagami, Tsumura, Wong and their collaborators. It is still the latest and greatest go-to source for information on quantum field theories in three dimensions (having nothing to say about the PoincarĂ© conjecture).

57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57N10 Topology of general \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
18D20 Enriched categories (over closed or monoidal categories)
18D35 Structured objects in a category (MSC2010)
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
Full Text: DOI