Fermat limit and congruence of Ohtsuki invariants

Details Fermat limit and congruence of Ohtsuki invariants Fermat limit and congruence of Ohtsuki invariants

1998-10-26

arxiv.org/abs/math/9810147v2

Geom. Topol. Monogr. 2 (1999), 321-333

Mathematics

Geometric Topology

13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper17.abs.html

Scientific paper

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.

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