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pro vyhledávání: '"Bodén, Hans"'
In this paper, we study alternating links in thickened surfaces in terms of the lattices of integer flows on their Tait graphs. We use this approach to give a short proof of the first two generalised Tait conjectures. We also prove that the flow latt
Externí odkaz:
http://arxiv.org/abs/2306.08971
Autor:
Boden, Hans U., Karimi, Homayun
A mock Seifert matrix is an integral square matrix representing the Gordon-Litherland form of a pair $(K,F)$, where $K$ is a knot in a thickened surface and $F$ is an unoriented spanning surface for $K$. Using these matrices, we introduce a new notio
Externí odkaz:
http://arxiv.org/abs/2301.05946
We construct two homology 3-spheres for which the (unperturbed) $SU(2)$ Chern-Simons function is not Morse-Bott. In one case, there is a degenerate isolated critical point. In the other, a path component of the critical set is not homeomorphic to a m
Externí odkaz:
http://arxiv.org/abs/2301.03676
Autor:
Boden, Hans U., Elmacioglu, Ceyhun, Guha, Anshul, Karimi, Homayun, Rushworth, William, Tang, Yun-chi, Jun, Bryan Wang Peng
We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon knotted surface of which K is a
Externí odkaz:
http://arxiv.org/abs/2209.15577
Autor:
Boden, Hans U., Karimi, Homayun
Publikováno v:
New York J. Math. 28 (2022) 1372-1398
We extend some classical results of Bankwitz, Crowell, and Murasugi to the setting of virtual links. For instance, we show that an alternating virtual link is split if and only if it is visibly split, and that the Alexander polynomial of any almost c
Externí odkaz:
http://arxiv.org/abs/2204.09767
Publikováno v:
In Journal of Sound and Vibration 5 February 2025 596
Autor:
Boden, Hans U., Karimi, Homayun
Using the Gordon-Litherland pairing, one can define invariants (signature, nullity, determinant) for ${\mathbb Z}/2$ null-homologous links in thickened surfaces. In this paper, we study the concordance properties of these invariants. For example, if
Externí odkaz:
http://arxiv.org/abs/2111.07409
Autor:
Boden, Hans U., Shimoda, Matthew
Publikováno v:
Ars Math. Cont., 23 (2023), no. 1
Given a knot, we develop methods for finding the braid representative that minimizes the number of simple walks. Such braids lead to an efficient method for computing the colored Jones polynomial of $K$, following an approach developed by Armond and
Externí odkaz:
http://arxiv.org/abs/2109.11483
Publikováno v:
Internat. J. Math. 33 (2022), 10n11, ID: 225078
We extend the Gordon-Litherland pairing to links in thickened surfaces, and use it to define signature, determinant, and nullity invariants for links that bound (unoriented) spanning surfaces. The invariants are seen to depend only on the $S^*$-equiv
Externí odkaz:
http://arxiv.org/abs/2107.00426
Autor:
Boden, Hans U., Rushworth, William
Publikováno v:
Bull. Lond. Math. Soc. 53 (2021), no. 4, 1174-1184
A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equivalence class of links in thickened surfaces. We prove that a minimal crossing virtual link diagram has minimal genus across representatives of the st
Externí odkaz:
http://arxiv.org/abs/2012.09000