Quantum invariants of knots and 3-manifolds

Autor*innen

• Vladimir Turaev

Parameter

• 608 Seiten
• 22 Lesestunden

• Mathematik

Mehr zum Buch

This monograph is now available in its third revised edition due to its strong appeal and wide use. It systematically explores 3-dimensional topological quantum field theories (TQFTs), building on the author's collaboration with N. Reshetikhin and O. Viro. The work is inspired by the Jones polynomial of knots and Witten-Chern-Simons field theory, with significant influences from braided categories and quantum groups. The book is structured into three parts. Part I constructs 3-dimensional TQFTs and 2-dimensional modular functors from modular categories, yielding a broad range of knot invariants and 3-manifold invariants, along with linear representations of mapping class groups of surfaces. In Part II, the 6j-symbols technique defines state sum invariants of 3-manifolds, linking them to the TQFTs from Part I through the theory of shadows. Part III presents constructions of modular categories, drawing from quantum groups and skein modules of tangles in 3-space. This essential contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with a foundation in basic algebra and topology. It serves as a crucial resource for those looking to engage with this intriguing intersection of mathematics and physics.

• Sprache: Englisch
• Erscheinungsdatum: 2016
• Einband: Hardcover