Donaldson–Frohman–Nicas TQFT identification conjecture

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Let VDF{\cal V}^{DF} be Donaldson's TQFT associated with moduli spaces of connections on a non-trivial SO(3)SO(3) bundle. For x1,x2,…x_1,x_2,\ldots, define

D=∑k≥1(k+13)xk∈P+.D=\sum_{k\geq 1}{k+1\choose 3}x_k\in{\cal P}^+.

Let V(D){\cal V}^{(D)} be the polynomial TQFT associated with DD. Donaldson–Frohman–Nicas conjecture.

VDF≅V(D).{\cal V}^{DF}\cong{\cal V}^{(D)}.

The source notes that equality already holds on vector spaces and invariants, while the claimed TQFT isomorphism remains the conjectural part.

References

Primary source

Thomas Kerler, “Homology TQFT's and the Alexander-Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory”, arXiv:math/0008204 (2002).

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