2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77606By 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 λ_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: λ_1=2λ_2 mod 24.13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper17.abs.htmlGeometric TopologyQuantum Algebra57M99, 57N10, 57M50text