Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 17, pages 321-333.

Fermat limit and congruence of Ohtsuki invariants

Xiao-Song Lin, Zhenghan Wang

Abstract. By calculating the Fermat limit of certain q-Fermat functions, we get explicit surgery formulae for the second and third Ohtsuki invariants for homology 3-spheres. The surgery formula of the second Ohtsuki invariant \lambda _2, combined with an argument using the general theory of finite type invariants of homology 3-spheres, leads to a congruence relation between the first and second Ohtsuki invariants: \lambda _1=2\lambda _2 mod 24.

Keywords. Fermat limit, homology 3-spheres, Ohtsuki invariants

AMS subject classification. Primary: 57M99. Secondary: 57N10, 57M50.

E-print: arXiv:math.GT/9810147

Submitted: 20 January 1999. (Revised: 10 October 1999.) Published: 20 November 1999.

Notes on file formats

Xiao-Song Lin, Zhenghan Wang

Department of Mathematics, University of California
Riverside, CA 92521, USA

Department of Mathematics, Indiana University
Bloomington, IN 47405, USA


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