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Abstract
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For rational homology
–spheres,
there exist two universal finite-type invariants: the Le–Murakami–Ohtsuki invariant
and the Kontsevich–Kuperberg–Thurston invariant. These invariants take values in
the same space of “Jacobi diagrams”, but it is not known whether they are equal. In
2004, Lescop proved that the KKT invariant satisfies some “splitting formulas” which
relate the variations of KKT under replacement of embedded rational homology
handlebodies by others in a “Lagrangian-preserving” way. We show that the LMO
invariant satisfies exactly the same relations. The proof is based on the LMO
functor, which is a generalization of the LMO invariant to the category of
–dimensional
cobordisms, and we generalize Lescop’s splitting formulas to this setting.
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Keywords
$3$–manifold, finite-type invariant, LMO invariant,
Lagrangian-preserving surgery
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Mathematical Subject Classification 2010
Primary: 57M27
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Publication
Received: 11 October 2013
Accepted: 15 April 2014
Published: 15 January 2015
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