Constructs a symmetric monoidal ∞-category of sheaves whose unit is geometric cobordism and canonically identifies its endomorphisms with the E∞-Thom spectrum.
On the Classification of Topological Field Theories
11 Pith papers cite this work. Polarity classification is still indexing.
11
Pith papers citing it
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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UNVERDICTED 11roles
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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.
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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.