Geometry & Topology Monographs, Vol. 7 (2004),
Proceedings of the Casson Fest,
Paper no. 9, pages 213--233.

Local surgery formulas for quantum invariants and the Arf invariant

Robion Kirby, Paul Melvin

Abstract. A formula for the Arf invariant of a link is given in terms of the singularities of an immersed surface bounded by the link. This is applied to study the computational complexity of quantum invariants of 3-manifolds.

Keywords. Arf invariants, quantum invariants, mu invariants, surgery, immersed surfaces, P/NP, complexity

AMS subject classification. Primary: 57M27. Secondary: 68Q15.

E-print: arXiv:math.AT/0410358

Submitted to GT on 15 October 2003. (Revised 2 January 2004.) Paper accepted 10 December 2003. Paper published 19 September 2004.

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Robion Kirby, Paul Melvin
University of California, Berkeley, CA 94720, USA
Bryn Mawr College, Bryn Mawr, PA 19010, USA
Email: kirby@math.berkeley.edu, pmelvin@brynmawr.edu

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