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.

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Patrick M Gilmer
Louisiana State University
Department of Mathematics
Baton Rouge, LA 70803, USA
Email: gilmer@math.lsu.edu

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