29 citations · 110 across the 27 of their papers we have counts for
31 papers
Modular Functors with Singularities from Vertex Operator Algebras Beyond Rigidity and Finiteness
Lukas Müller, Lukas Woike
For a vertex operator algebra and a certain category of its modules, we propose a construction for spaces of conformal blocks organized into an open-closed modular functor with…
Pivotal Module Categories, Factorization Homology and Modular Invariant Modified Traces
Jorge Becerra, Lukas Woike
The algebraic notion of a pivotal module category was developed by Schaumann and Shimizu and is central to the description of boundary conditions in conformal field theory accordin…
The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory
Lukas Woike
For logarithmic conformal field theories whose monodromy data is given by a not necessarily semisimple modular category, we solve the problem of constructing and classifying the co…
Reflection Equivariance and the Heisenberg Picture for Spaces of Conformal Blocks
Lukas Woike
Monoidal product, braiding, balancing and weak duality are pieces of algebraic information that are well-known to have their origin in oriented genus zero surfaces and their mappin…
Modular functors from conformal blocks of rational vertex operator algebras
Chiara Damiolini, Lukas Woike
For a vertex operator algebra , one may naturally define spaces of conformal blocks following a construction of Frenkel-Ben-Zvi generalized by Damiolini-Gibney-Tarasca. If i…
Admissible Skein Modules and Ansular Functors: A Comparison
Lukas Müller, Lukas Woike
Given a finite ribbon category, there are two possibilities for an extension defined on all three-dimensional handlebodies: On the one hand, one can use the admissible skein module…
The Cyclic and Modular Microcosm Principle in Quantum Topology
Lukas Woike
Monoidal categories with additional structure such as a braiding or some form of duality abound in quantum topology. They often appear in tandem with Frobenius algebras inside them…
Categorified Open Topological Field Theories
Lukas Müller, Lukas Woike
In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equippe…
The Lyubashenko Modular Functor for Drinfeld Centers via Non-Semisimple String-Nets
Lukas Müller, Christoph Schweigert, Lukas Woike +1
The Levin-Wen string-nets of a spherical fusion category describe, by results of Kirillov and Bartlett, the representations of mapping class groups of closed surfaces…
The Dehn Twist Action for Quantum Representations of Mapping Class Groups
Lukas Müller, Lukas Woike
We calculate the Dehn twist action on the spaces of conformal blocks of a not necessarily semisimple modular category. In particular, we give the order of the Dehn twists under the…
A Classification of Modular Functors via Factorization Homology
Adrien Brochier, Lukas Woike
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be descri…
The distinguished invertible object as ribbon dualizing object in the Drinfeld center
Lukas Müller, Lukas Woike
We prove that the Drinfeld center of a pivotal finite tensor category comes with the structure of a ribbon Grothendieck-Verdier category in the sense…
Homotopy Invariants of Braided Commutative Algebras and the Deligne Conjecture for Finite Tensor Categories
Christoph Schweigert, Lukas Woike
It is easy to find algebras in a finite tensor category that naturally come with a lift to a braided commutative algebra $\mathsf{T}\in Z(\…
Classification of Consistent Systems of Handlebody Group Representations
Lukas Müller, Lukas Woike
The classifying spaces of handlebody groups form a modular operad. Algebras over the handlebody operad yield systems of representations of handlebody groups that are compatible wit…
The Diffeomorphism Group of the Solid Closed Torus and Hochschild Homology
Lukas Müller, Lukas Woike
We prove that for a self-injective ribbon Grothendieck-Verdier category in the sense of Boyarchenko-Drinfeld the cyclic action on the Hochschild complex of $\mathcal{…
The differential graded Verlinde Formula and the Deligne Conjecture
Christoph Schweigert, Lukas Woike
A modular category gives rise to a differential graded modular functor, i.e. a system of projective mapping class group representations on chain complexes. This diffe…
The Trace Field Theory of a Finite Tensor Category
Christoph Schweigert, Lukas Woike
Given a finite tensor category , we prove that a modified trace on the tensor ideal of projective objects can be obtained from a suitable trivialization of the Nakayam…
Cyclic framed little disks algebras, Grothendieck-Verdier duality and handlebody group representations
Lukas Müller, Lukas Woike
We characterize cyclic algebras over the associative and the framed little 2-disks operad in any symmetric monoidal bicategory. The cyclicity is appropriately treated in a coherent…
Homotopy Coherent Mapping Class Group Actions and Excision for Hochschild Complexes of Modular Categories
Christoph Schweigert, Lukas Woike
Given any modular category over an algebraically closed field , we extract a sequence of -bimodules. We show that the Hochschild cha…
Dimensional Reduction, Extended Topological Field Theories and Orbifoldization
Lukas Müller, Lukas Woike
We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our de…
Categorification of algebraic quantum field theories
Marco Benini, Marco Perin, Alexander Schenkel +1
This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary…
The Hochschild Complex of a Finite Tensor Category
Christoph Schweigert, Lukas Woike
Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already dec…
The Little Bundles Operad
Lukas Müller, Lukas Woike
Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy qu…
Equivariant Higher Hochschild Homology and Topological Field Theories
Lukas Müller, Lukas Woike
We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group . As coefficients, we allow -algebras with -acti…