**Holomorphic invariants of 3-manifolds and q-gamma
functions**

**Ruth Lawrence**

**Abstract: ** We give a procedure which it is conjectured will reconstruct an invariant, Z^0(M), of rational homology 3-spheres, M, which is defined as a holomorphic function of a parameter q. It is defned in a way similar to the sl_2 Witten-Reshetikhin-Turaev invariant, Z_K(M), an invariant defined only at roots of unity q with q^K=1. It is believed that Z^0(M) is related to the trivial connection contribution to the stationary phase expansion of the Feynman integral form for Z_K(M) and that they share many other properties, which will be investigated in a forthcoming paper.

**Length: **22 pages

**Reference: **In preparation.

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*Last updated on April 15th, 2018.*

ruthel@ma.huji.ac.il