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

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.