15 citations · 41 across the 12 of their papers we have counts for
8 papers · 1 filter
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…
An algebraic property of Reidemeister torsion
Teruaki Kitano, Yuta Nozaki
For a 3-manifold and an acyclic -representation of its fundamental group, the -Reidemeister torsion $τ_ρ(M) \in \mathb…
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…
Filtered instanton Floer homology and the homology cobordism group
Yuta Nozaki, Kouki Sato, Masaki Taniguchi
For any and oriented homology 3-sphere , we introduce a homology cobordism invariant . The values are included in the cr…
Finiteness of the image of the Reidemeister torsion of a splice
Teruaki Kitano, Yuta Nozaki
The set of values of the -Reidemeister torsion of a 3-manifold can be both finite and infinite. We prove that is a…
Every lens space contains a genus one homologically fibered knot
Yuta Nozaki
We prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof,…
An extension of the LMO functor
Yuta Nozaki
Cheptea, Habiro and Massuyeau constructed the LMO functor, which is defined on a certain category of cobordisms between two surfaces with at most one boundary component. In this pa…