#### Geometry & Topology Monographs 2 (1999),
Proceedings of the Kirbyfest,
paper no. 9, pages 157-175.

## Quantum Invariants of periodic three-manifolds

### Patrick M Gilmer

**Abstract**.
Let p be an odd prime and r be relatively prime to p. Let G be a
finite p-group. Suppose an oriented 3-manifold M-tilde has a free
G-action with orbit space M. We consider certain
Witten-Reshetikhin-Turaev SU(2) invariants w_r(M). We will give a
fomula for w_r(M) in terms of the defect of M-tilde --> M and the
number of elements in G. We also give a version of this result if M
and M-tilde contain framed links or colored fat graphs. We give
similar formulas for non-free actions which hold for a specified
finite set of values for r.
**Keywords**.
p-group action, lens space, quantum invariant, Turaev-Viro invariant, branched cover, Jones polynomial, Arf invariant

**AMS subject classification**.
Primary: 57M10.
Secondary: 57M12.

**E-print:** `arXiv:math.GT/9902122`

Submitted: 23 February 1999.
(Revised: 26 May 1999.)
Published: 18 November 1999.

Notes on file formats
Patrick M Gilmer

Louisiana State University

Department of Mathematics

Baton Rouge, LA 70803, USA

Email: gilmer@math.lsu.edu

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