Geometric Topology and Field Theory on 3-Manifolds

DOI10.1007/978-3-642-15637-3_8zbMath1221.57023OpenAlexW1530502791MaRDI QIDQ3078615

Kishore B. Marathe

Publication date: 28 February 2011

Published in: The Mathematics of Knots (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-15637-3_8

zbMATH Keywords

Morse theorytopological field theoryChern-Simons theoryCasson invariantknot invariantsKhovanov homologytopological quantum field theoryWitten-Reshetikhin-Turaev invariantsgeometrization conjectureKhovanov polynomialFukaya-Floer homologytopological quantum gravity

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Topological field theories in quantum mechanics (81T45) Topological quantum field theories (aspects of differential topology) (57R56) Eta-invariants, Chern-Simons invariants (58J28)

Cites Work

• Topological quantum field theories
• Branes and quantization
• Morse homology
• Fusion rules and modular transformations in 2D conformal field theory
• A complete proof of the Poincaré and geometrization conjectures -- application of the Hamilton-Perelman theory of the Ricci flow
• Chern-Simons and string theory
• Casson's invariant and gauge theory
• Topological gauge theories and group cohomology
• Exact results for perturbative Chern-Simons theory with complex gauge group
• State models and the Jones polynomial
• Four-manifolds with positive curvature operator
• The Yang-Baxter equation and invariants of links
• Topological quantum field theory
• A proof of the mock theta conjectures
• Current algebras and Wess-Zumino model in two dimensions
• Quantum field theory and the Jones polynomial
• Witten's complex and infinite dimensional Morse theory
• Supersymmetry and Morse theory
• The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\)
• Perturbative expansion of Chern-Simons theory with non-compact Gauge group
• Topological invariants for 3-manifolds using representations of mapping class groups. I
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• Topological gravity as large \(N\) topological gauge theory
• Braids and invariants of 3-manifolds
• Skeins and quantum \(SU(N)\) invariants of 3-manifolds
• Heegaard Floer homology and alternating knots
• Modular forms and quantum invariants of \(3\)-manifolds
• On Khovanov's categorification of the Jones polynomial
• Integral invariants of 3-manifolds. II.
• Symplectic conifold transitions.
• Infinite dimensional Morse theory and multiple solution problems
• Monstrous moonshine and monstrous Lie superalgebras
• Hecke algebras, modular categories and 3-manifolds quantum invariants
• The Euler characteristic of the moduli space of curves
• The geometry of gauge fields
• An instanton-invariant for 3-manifolds
• Three-manifolds with positive Ricci curvature
• All loop topological string amplitudes from Chern-Simons theory
• Hodge integrals and degenerate contributions
• A categorification of the Jones polynomial
• Invariants of 3-manifolds via link polynomials and quantum groups
• Topological string partition functions as equivariant indices
• Quantization of Chern-Simons gauge theory with complex gauge group
• 2-d physics and 3-d topology
• QUANTUM INVARIANTS OF 3-MANIFOLDS ASSOCIATED WITH CLASSICAL SIMPLE LIE ALGEBRAS
• The volume conjecture and topological strings
• The Superpolynomial for Knot Homologies
• Instanton Homology of Seifert Fibred Homology Three Spheres
• Morse Theory, the Conley Index and Floer Homology
• Topics in Physical Mathematics
• Links, quantum groups and TQFTs
• General Relativity for Mathematicians
• QuantumSU(2)-invariants dominate Casson'sSU(2)-invariant
• On the self-linking of knots
• Topological quantum field theories from subfactors
• The Yang-Mills equations over Riemann surfaces
• RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE
• Lectures on the topology of 3-manifolds. An introduction to the Casson invariant
• Quantum invariants of knots and 3-manifolds
• On the gauge theory/geometry correspondence
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item