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Invariants of Piecewise-Linear 3-Manifolds
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In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple involutory Hopf algebra. The invariant is defined by a state sum model on a triangulation. In some cases, the invariant is the partition function of a topological quantum field theory.
Forward citations
Cited by 14 Pith papers
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Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging
Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
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Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
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Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
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Deferred Cyclotomic Representation for Stable and Exact Evaluation of q-Hypergeometric Series
The deferred cyclotomic representation (DCR) is a parameter-independent combinatorial object for q-hypergeometric series that resolves numerator-denominator cancellations exactly as integer arithmetic prior to evaluat...
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On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
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Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.
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Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
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Symmetry, Symmetry Topological Field Theory and von Neumann Algebra
The symmetric-sector von Neumann algebra of a QFT violates additivity or Haag duality exactly when the Lagrangian algebra of its SymTFT contains operators beyond the identity, with a sharper criterion distinguishing t...
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Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
In (2+1)d abelian lattice gauge theories, a twisted-gauging duality is realized by tensor networks, and the permutation of topological sectors is computed, yielding unitary maps between dual Hamiltonians.
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ASEP/DSSYK duality and strange correlator
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
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Unitary Categorical Symmetries
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Categorical quantum symmetries and ribbon tensor 2-categories
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
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Les Houches Lecture Notes on Tensor Networks
A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.
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