4 citations · 4 across the 5 of their papers we have counts for
6 papers
The homology cobordism group is not generated by graph homology -spheres
Ben Mares, Yuta Nozaki, Masaki Taniguchi
We show the homology cobordism group of homology -spheres is not generated by graph homology -spheres. Our technique is a combination of filtered instanton Floer theory and G…
Analysis of Hopf solitons as generalized fold maps
Yuta Nozaki, Darian Hall, Ivan I. Smalyukh +1
The Hopf index, a topological invariant that quantifies the linking of preimage fibers, is fundamental to the structure and stability of hopfions. In this work, we propose a new ma…
Homotopy classification of knotted defects in bounded domains
Yuta Nozaki, David Palmer, Yuya Koda
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…
Quantum Knots that Never Come Untied
Michikazu Kobayashi, Yuta Nozaki, Yuya Koda +1
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…
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…
Homotopy classification of knotted defects in ordered media
Yuta Nozaki, Tamás Kálmán, Masakazu Teragaito +1
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…