A surgery formula for the 2-loop piece of the LMO invariant of a pair
Andrew Kricker
Abstract
Let Θ(M,K) denote the 2-loop piece of (the logarithm of) the LMO invariant of a knot K in M, a ZHS3. Forgetting the knot (by which we mean setting diagrams with legs to zero) specialises Θ(M,K) to λ(M), Casson's invariant. This note describes an extension of Casson's surgery formula for his invariant to Θ(M,K). To be precise, we describe the effect on Θ(M,K) of a surgery on a knot which together with K forms a boundary link in M. Whilst the presented formula does not characterise Θ(M,K), it does allow some insight into the underlying topology.
Create a lesson
Related papers
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
Nancy Scherich, Nathaniel Song
The flip symmetry on Khovanov-Rozansky homology
Hongjian Yang
Families of knots that cannot be made Legendrian parametrically
Javier Martínez-Aguinaga
Branched real projective structures on surfaces and geometrisation of representations
Gianluca Faraco, Nicholas Rungi
Generating the twist subgroup of the level 2 mapping class group of a non-orientable closed surface
Ryoma Kobayashi
H-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Sungkyung Kang, JungHwan Park, Masaki Taniguchi