Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Nozaki, Yuta"'
Nozaki et.~al.\ gave a homotopy classification of the knotted defects of ordered media in three-dimensional space by considering continuous maps from complements of spatial graphs to the order parameter space modulo a certain equivalence relation. We
Externí odkaz:
http://arxiv.org/abs/2411.03918
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
Lord Kelvin proposed that atoms form hydrodynamic vortex knots. However, they typically untie through reconnections, i. e., local cut-and-slice events, unlike stable vortex unknots such as smoke rings. The same holds in superfluids--quantum fluids wi
Externí odkaz:
http://arxiv.org/abs/2410.07470
For simple graphs $G$ and $H$, the Hom complex $\mathrm{Hom}(G,H)$ is a polyhedral complex whose vertices are the graph homomorphisms $G\to H$. It is known that $\mathrm{Hom}(G,H)$ is homotopy equivalent to a disjoint union of points and circles when
Externí odkaz:
http://arxiv.org/abs/2408.04802
Autor:
Hatano, Tomoaki, Nozaki, Yuta
For classical knots, it is well known that their determinants mod $8$ are classified by the Arf invariant. Boden and Karimi introduced a determinant of checkerboard colorable virtual knots. We prove that their determinant mod $8$ is classified by the
Externí odkaz:
http://arxiv.org/abs/2408.01891
In the study of ribbon knots, Lamm introduced symmetric unions inspired by earlier work of Kinoshita and Terasaka. We show an identity between the twisted Alexander polynomials of a symmetric union and its partial knot. As a corollary, we obtain an i
Externí odkaz:
http://arxiv.org/abs/2407.09881
A ladder lottery, known as ``Amidakuji'' in Japan, is a common way to decide an assignment at random. In this paper, we investigate reconfiguration and enumeration problems of cyclic ladder lotteries. First, when a permutation $\pi$ and an optimal di
Externí odkaz:
http://arxiv.org/abs/2405.16408
We give a homotopy classification of the global defects in ordered media, and explain it via the example of biaxial nematic liquid crystals, i.e., systems where the order parameter space is the quotient of the $3$-sphere $S^3$ by the quaternion group
Externí odkaz:
http://arxiv.org/abs/2402.16079
Autor:
Ito, Takehiro, Kakimura, Naonori, Kamiyama, Naoyuki, Kobayashi, Yusuke, Maezawa, Shun-ichi, Nozaki, Yuta, Okamoto, Yoshio
We prove that the computation of a combinatorial shortest path between two vertices of a graph associahedron, introduced by Carr and Devadoss, is NP-hard. This resolves an open problem raised by Cardinal. A graph associahedron is a generalization of
Externí odkaz:
http://arxiv.org/abs/2304.14782
Autor:
Ito, Takehiro, Iwamasa, Yuni, Kobayashi, Yusuke, Maezawa, Shun-ichi, Nozaki, Yuta, Okamoto, Yoshio, Ozeki, Kenta
In 1973, Fisk proved that any $4$-coloring of a $3$-colorable triangulation of the $2$-sphere can be obtained from any $3$-coloring by a sequence of Kempe-changes. On the other hand, in the case where we are only allowed to recolor a single vertex in
Externí odkaz:
http://arxiv.org/abs/2210.17105