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pro vyhledávání: '"Suzuki, Masaaki"'
Clasper surgery induces the $Y$-filtration $\{Y_n\mathcal{IC}\}_n$ over the monoid of homology cylinders, which serves as a $3$-dimensional analogue of the lower central series of the Torelli group of a surface. In this paper, we investigate the tors
Externí odkaz:
http://arxiv.org/abs/2410.10061
Autor:
Morifuji, Takayuki, Suzuki, Masaaki
The twisted Alexander polynomial of a knot is defined associated to a linear representation of the knot group. If there exists a surjective homomorphism of a knot group onto a finite group, then we obtain a representation of the knot group by the com
Externí odkaz:
http://arxiv.org/abs/2311.15484
Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the twisted Alexander vanishing order of a knot to be the order of the smallest finite group such that the corresponding twisted Alexander polynomial is zero. In
Externí odkaz:
http://arxiv.org/abs/2310.10936
Autor:
Suzuki, Masaaki, Tran, Anh T.
In this paper, we consider two properties on the braid index of a two-bridge knot. We prove an inequality on the braid indices of two-bridge knots if there exists an epimorphism between their knot groups. Moreover, we provide the average braid index
Externí odkaz:
http://arxiv.org/abs/2310.02483
It is well-known that a knot is Fox $n$-colorable for a prime $n$ if and only if the knot group admits a surjective homomorphism to the dihedral group of degree $n$. However, this is not the case for links with two or more components. In this paper,
Externí odkaz:
http://arxiv.org/abs/2302.13706
Publikováno v:
International Journal of Mathematics, 35, (2024), 2450052 (24 pages)
A lower bound of the Gordian distance is presented in terms of the Blanchfield pairing. Our approach, in particular, allows us to show at least for 195 pairs of unoriented nontrivial prime knots with up to 10 crossings that their Gordian distance is
Externí odkaz:
http://arxiv.org/abs/2208.13327
Publikováno v:
Trans. Amer. Math. Soc., electronically published on April 19, 2023
We compute the Reidemeister-Turaev torsion of homology cylinders which takes values in the $K_1$-group of the $I$-adic completion of the group ring $\mathbb{Q}\pi_1\Sigma_{g,1}$, and prove that its reduction to $\widehat{\mathbb{Q}\pi_1\Sigma_{g,1}}/
Externí odkaz:
http://arxiv.org/abs/2206.13019
Autor:
Suzuki, Masaaki, Tran, Anh T.
In this paper, we determine the average genus of all the $2$-bridge knots with a given crossing number. As a consequence, we obtain the oblique asymptote of this value as the crossing number grows.
Comment: 18 pages, 1 table
Comment: 18 pages, 1 table
Externí odkaz:
http://arxiv.org/abs/2204.09238
Publikováno v:
J. Topol. 15 (2022) 587-619
Every homology cylinder is obtained from Jacobi diagrams by clasper surgery. The surgery map $\mathfrak{s} \colon \mathcal{A}_n^c \to Y_n\mathcal{IC}_{g,1}/Y_{n+1}$ is surjective for $n \geq 2$, and its kernel is closely related to the symmetry of Ja
Externí odkaz:
http://arxiv.org/abs/2103.07086
Autor:
Suzuki, Masaaki
We have the generating function which determines the number of $2$-bridge knot groups admitting epimorphisms onto the knot group of a given $2$-bridge knot, in terms of crossing number. In this paper, we will refine this formula by taking account int
Externí odkaz:
http://arxiv.org/abs/2010.06832