Fermat limit and congruence of Ohtsuki invariants

1998/10/31 by Xiao-Song Lin, Zhenghan Wang
Mathematics · #math.GT #math.QA #msc:57M99 #msc:57N10 #msc:57M50

paper · pdf

published as Geom. Topol. Monogr. 2 (1999), 321-333 · 13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper17.abs.html

arxiv created 1999/11/20 · arxiv updated 2009/11/30

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.

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