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Fermat limit and congruence of Ohtsuki invariants

Xiao-Song Lin and Zhenghan Wang

Geometry & Topology Monographs 2 (1999) 321–333

DOI: 10.2140/gtm.1999.2.321

arXiv: math.GT/9810147

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 λ2, 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: λ1= 2λ2 mod 24.

Dedicated to Rob Kirby on the occasion of his 60th birthday.

Keywords

Fermat limit, homology 3–spheres, Ohtsuki invariants

Mathematical Subject Classification

Primary: 57M99

Secondary: 57M50, 57N10

References
Publication

Received: 20 January 1999
Revised: 10 October 1999
Published: 20 November 1999

Authors
Xiao-Song Lin
Department of Mathematics
University of California
Riverside CA 92521
USA
Zhenghan Wang
Department of Mathematics
Indiana University
Bloomington IN 47405
USA