Semisimple four‐dimensional topological field theories cannot detect exotic smooth structure

DOI10.1112/topo.12288arXiv2001.02288OpenAlexW4364361459WikidataQ122485690 ScholiaQ122485690MaRDI QIDQ6048710

David Reutter

Publication date: 15 September 2023

Published in: Journal of Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.02288

zbMATH Keywords

TQFT

Mathematics Subject Classification ID

Topological field theories in quantum mechanics (81T45) Topological quantum field theories (aspects of differential topology) (57R56) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Fusion categories, modular tensor categories, modular functors (18M20) Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants) (57K41)

Related Items

Drinfel'd double symmetry of the 4d Kitaev model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topological quantum field theories
• The topology of four-dimensional manifolds
• The stable topology of 4-manifolds
• Universal manifold pairings and positivity
• On braided fusion categories. I
• Stable diffeomorphism of compact 4-manifolds
• Computer calculation of Witten's 3-manifold invariant
• Surgery and duality
• Tori detect invertibility of topological field theories
• Dichromatic state sum models for four-manifolds from pivotal functors
• An application of gauge theory to four dimensional topology
• Monopoles and four-manifolds
• Invariants of 3-manifolds via link polynomials and quantum groups
• Four dimensional topological quantum field theories from \(G\)-crossed braided categories
• Holomorphic triangles and invariants for smooth four-manifolds
• Separable algebras over commutative rings
• Fermionic modular categories and the 16-fold way
• Positivity of topological field theories in dimension at least 5
• Positivity of the universal pairing in 3 dimensions
• On the Classification of Topological Field Theories
• Handlebody decompositions of complex surfaces
• The Embedding of Two-Spheres in the Four-Sphere
• Classification and construction of unitary topological field theories in two dimensions
• State-Sum Invariants of 4-Manifolds
• S-Structures for k -Linear Categories and the Definition of a Modular Functor
• Higher-dimensional algebra and topological quantum field theory
• Direct sum decompositions and indecomposable TQFTs
• A new description of orthogonal bases
• Tensor Categories
• On Simply-Connected 4-Manifolds
• On dualizability of braided tensor categories