Donaldson–Frohman–Nicas TQFT identification conjecture

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=k1(k+13)xkP+.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.

VDFV(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.

Sources & referencesView supporting material

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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