#### 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

Email: xl@math.ucr.edu, zhewang@indiana.edu

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