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15 papers · 1 filter
Torsion elements in the associated graded of the -filtration of the monoid of homology cylinders
Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki
Clasper surgery induces the -filtration over the monoid of homology cylinders, which serves as a -dimensional analogue of the lower central series of…
A non-commutative Reidemeister-Turaev torsion of homology cylinders
Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki
We compute the Reidemeister-Turaev torsion of homology cylinders which takes values in the -group of the -adic completion of the group ring , and prov…
On the kernel of the surgery map restricted to the 1-loop part
Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki
Every homology cylinder is obtained from Jacobi diagrams by clasper surgery. The surgery map is surjective f…
Abelian quotients of the -filtration on the homology cylinders via the LMO functor
Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki
We construct a series of homomorphisms from the -filtration on the monoid of homology cylinders to torsion modules via the mod reduction of the LMO functor. The res…
Profinite rigidity for twisted Alexander polynomials
Jun Ueki
We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the…
When is a band-connected sum equal to the connected sum?
Katura Miyazaki
We show that a band-connected sum of knots and along a band is equal to the connected sum if and only if is a trivial band.