There is a presentably symmetric monoidal stable infinity-category of homotopy-invariant Gysin sheaves whose unit is geometric cobordism and whose endomorphism E-infinity ring is the associated Thom spectrum.
On the Classification of Topological Field Theories
11 Pith papers cite this work, alongside 6 external citations. Polarity classification is still indexing.
11
Pith papers citing it
6
external citations · Pith
abstract
This paper provides an informal sketch of a proof of the Baez-Dolan cobordism hypothesis, which provides a classification for extended topological quantum field theories.
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Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
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.
Defines the three-variable superalgebra series F_K(y,z,q) for knot complements, derives its surgery relation to hat Z(q), and computes examples for torus knots.
Hermitian forms on Hilbert spaces arise from the monoid structure of complex conjugation in Z/2-equivariant real linear types within LHoTT, requiring only a negative unit term.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
Proposes axiomatic framework for derived skein modules of 3-manifolds that recovers ordinary skein modules in degree zero, with computable formulas, Hochschild formula for Sigma x S^1, first computations, and finiteness via deformation quantization.
The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
Introduces G-Hermitian 2-vector spaces via fixed points of an O(2)-action on 2Vect and criteria for positive pairings to generalize the Hermitian-to-Hilbert passage, with an outline for inductive higher-dimensional versions.
citing papers explorer
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A homotopy coherent Pontryagin-Thom isomorphism
There is a presentably symmetric monoidal stable infinity-category of homotopy-invariant Gysin sheaves whose unit is geometric cobordism and whose endomorphism E-infinity ring is the associated Thom spectrum.
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Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function
Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
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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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A supergroup series for knot complements
Defines the three-variable superalgebra series F_K(y,z,q) for knot complements, derives its surgery relation to hat Z(q), and computes examples for torus knots.
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Quantum and Reality
Hermitian forms on Hilbert spaces arise from the monoid structure of complex conjugation in Z/2-equivariant real linear types within LHoTT, requiring only a negative unit term.
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Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
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Derived skein module
Proposes axiomatic framework for derived skein modules of 3-manifolds that recovers ordinary skein modules in degree zero, with computable formulas, Hochschild formula for Sigma x S^1, first computations, and finiteness via deformation quantization.
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Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation
The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
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Candidate Gaugings of Categorical Continuous Symmetry
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
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Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
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The many faces of higher Hilbert spaces
Introduces G-Hermitian 2-vector spaces via fixed points of an O(2)-action on 2Vect and criteria for positive pairings to generalize the Hermitian-to-Hilbert passage, with an outline for inductive higher-dimensional versions.