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Tetrahedral forms in monoidal categories and 3-manifold invariants
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Nathan Geer
,
Rinat Kashaev
Published/Copyright:
December 13, 2011
Abstract
We introduce systems of objects and operators in linear monoidal categories called Ψ̂-systems. A Ψ̂-system satisfying several additional assumptions gives rise to a topological invariant of triples (a closed oriented 3-manifold M, a principal bundle over M, a link in M). This construction generalizes the quantum dilogarithmic invariant of links appearing in the original formulation of the volume conjecture. We conjecture that all quantum groups at odd roots of unity give rise to Ψ̂-systems and we verify this conjecture in the case of the Borel subalgebra of quantum 𝔰𝔩2.
Received: 2010-08-27
Revised: 2011-04-20
Published Online: 2011-12-13
Published in Print: 2012-12
©[2012] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- An upper bound on the exceptional characteristics for Lusztig's character formula
- Equivariant Kählerian extensions of contact manifolds
- On the dimension of CAT(0) spaces where mapping class groups act
- Tetrahedral forms in monoidal categories and 3-manifold invariants
- Continuity of the Álvarez class under deformations
- Colocalizing subcategories and cosupport
- Dunkl operator and quantization of ℤ2-singularity
- An even unimodular 72-dimensional lattice of minimum 8
