Zobrazeno 1 - 10
of 712
pro vyhledávání: '"57Q45"'
Autor:
Kawauchi, Akio
Free ribbon lemma that every free sphere-link in the 4-sphere is a ribbon sphere-link is shown in an earlier paper by the author. In this paper, another proof of this lemma is given.
Externí odkaz:
http://arxiv.org/abs/2408.04793
Autor:
Kawauchi, Akio
The $k$th module of a surface-knot of a genus $g$ in the 4-sphere is the $k$th integral homology module of the infinite cyclic covering of the surface-knot complement. The reduced first module is the quotient module of the first module by the finite
Externí odkaz:
http://arxiv.org/abs/2408.04285
A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily oriented. In this
Externí odkaz:
http://arxiv.org/abs/2401.14143
Autor:
Fukuda, Mizuki, Ishikawa, Masaharu
A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of
Externí odkaz:
http://arxiv.org/abs/2304.06276
Autor:
Kawauchi, Akio
Whitehead aspherical conjecture says that every connected subcomplex of every aspherical 2-complex is aspherical. By an argument on ribbon sphere-links, it is confirmed that the conjecture is true for every contractible finite 2-complex. In this pape
Externí odkaz:
http://arxiv.org/abs/2303.04368
Autor:
Kawauchi, Akio
M. A. Kervaire showed that every group of deficiency $d$ and weight $d$ is the fundamental group of a smooth sphere-link of $d$ components in a smooth homotopy 4-sphere. In the use of the smooth unknotting conjecture and the smooth 4D Poincar{\'e} co
Externí odkaz:
http://arxiv.org/abs/2212.02617
Autor:
Fukuda, Mizuki
It is known that a presentation of the knot group of a branched twist spin is obtained from a Wirtinger presentation of the original 1-knot group by adding a generator corresponding to a regular orbit of the circle action and a certain relator. In pa
Externí odkaz:
http://arxiv.org/abs/2209.11583
Autor:
Kawauchi, Akio
The classical Poincar{\'e} conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston's program on geometrizations of 3-manifolds. A new confirmation of this conjecture is given
Externí odkaz:
http://arxiv.org/abs/2103.16001
Autor:
Winter, Blake K
Satoh has defined a map from virtual knots to ribbon surfaces embedded in $S^4$. Herein, we generalize this map to virtual $m$-links, and use this to construct generalizations of welded and extended welded knots to higher dimensions. This also allows
Externí odkaz:
http://arxiv.org/abs/2103.08766
Every embedded surface $\mathcal{K}$ in the 4-sphere admits a bridge trisection, a decomposition of $(S^4,\mathcal{K})$ into three simple pieces. In this case, the surface $\mathcal{K}$ is determined by an embedded 1-complex, called the $\textit{1-sk
Externí odkaz:
http://arxiv.org/abs/2007.07280