The identification of the unframed invariant with the LMO invariant

About 27 years old · traced to

Let MM be an integer homology 33-sphere, let I~n(M)\widetilde{I}_n(M) be the decoration-independent unframed invariant obtained by subtracting the framing correction from In(M)I_n(M), and set

ω(M)=∑nmnI~n(M),\omega(M)=\sum_n m^n\widetilde{I}_n(M),

where m=∣H1(M;Z)∣m=|H_1(M;\mathbb{Z})|. LMO identification conjecture. The invariant ω(M)\omega(M) equals the surgery-defined invariant of Le, Murakami, and Ohtsuki. This is equivalent to asserting that I~n\widetilde{I}_n satisfies the Le–Murakami–Ohtsuki surgery formula. The paper states that the equality is known to highest order because both invariants are universal, but the full identification remains unproved.

References

Primary source

Greg Kuperberg and Dylan P. Thurston, “Perturbative 3-manifold invariants by cut-and-paste topology”, arXiv:math/9912167 (2000).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.