Frobenius Algebras and 2-D Topological Quantum Field Theories

By Joachim Kock. 2004

508 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/110b05202f42028e9eabe6b038f7246040890f77

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Citations in the corpus

Interacting quantum observables: categorical algebra and diagrammatics (2009, background): “When the monoidal structure is strict, something which is of course always the case in graphical representation, observable structures obey the following remarkable theorem [29,11] – similar results are known for concrete †-Frobenius algebras, for example, for 2D topological quantum field theories, ”
Highest weight categories arising from Khovanov's diagram algebra II: Koszulity (2008, unknown): “x]/(x2) whose multiplication and comultiplication are deﬁned by the formulae (3.4)–(3.5) deﬁnes a 2-dimensional TQFT, that is, a symmetric monoidal functor F: 2-Cob →Vec. (3.6) We refer the reader to [K] for the detailed construction of F, just noting here that it takes a disjoint union X1⊔···⊔Xr of”
Highest Weight Categories Arising from Khovanov's Diagram Algebra I: Cellularity (2008, background): “6) We refer the reader to [K] for the detailed construction of F , just noting here that it takes a disjoint union X1t· · ·tXr of r copies of S1 to the tensor product of r copies of the vector space F[x]/(x2).”
A link-splitting spectral sequence in Khovanov homology (2013, methodology): “A (1 + 1)-dimensional TQFT is determined by commutative Frobenius algebra [10].”
The local Gromov-Witten theory of curves (2004, background): “Our discussion follows Sections 2 and 4 of [5] and draws from Chapter 1 of [14].”
Tensor categories: a selective guided tour (2008, background): “By the classification of TQFTs in 1+ 1 dimensions [65, 1, 156], this TQFT corresponds to a commutative Frobenius algebra B (in Vect k ), with A = V (S (1)) and the product arising from the pants cobordism.”
Categories for the practising physicist (2009, background): “Theorem 4. [ 39 ] The category 2TQFTK is equivalent to the category CFCK.”
K3 surfaces with Picard number one and infinitely many rational points (2005, background): “As an excellent and elementary reference for two-dimensional topological quantum field theories in mathematics we mention [Kock 2004].”
Quantum picturalism (2009, background): “Following Atiyah in [75], topological quantum field theories can be succinctly defined as monoidal functors from nCob into FHilb, where a functor is a map both on objects and on morphisms which preserves composition and tensor [22,23,76].”
Knot invariants and higher representation theory II: the categorification of quantum knot invariants (2010, methodology): “[Koc04] Joachim Kock, Frobenius algebras and 2D topological quantum field theories, London Mathematical Society Student Texts, vol. 59, Cambridge University Press, Cambridge, 2004.”
Knot Invariants and Higher Representation Theory (2013, methodology): “MR 2763732 (2012a:17021) [Koc04] Joachim Kock, Frobenius algebras and 2D topological quantum field theories, London Mathematical Society Student Texts, vol. 59, Cambridge University Press, Cambridge, 2004.”