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pro vyhledávání: '"57k10, 57n70"'
Autor:
Conway, Anthony, Miller, Allison N.
This article is concerned with locally flatly immersed surfaces in simply-connected $4$-manifolds where the complement of the surface has fundamental group $\mathbb{Z}$. Once the genus and number of double points are fixed, we classify such immersed
Externí odkaz:
http://arxiv.org/abs/2410.04635
Autor:
Fung, Antony T. H.
The Cyclic Surgery Theorem and Moser's work on surgeries on torus knots imply that for any non-trivial knot in $S^3$, there are at most two integer surgeries that produce a lens space. This paper investigates how many positive integer surgeries on a
Externí odkaz:
http://arxiv.org/abs/2405.11736
Autor:
Gabbard, Malcolm
In this paper we define the equivariant double-slice genus and equivariant super-slice genus of a strongly invertible knot. We prove lower bounds for both the equivariant double-slice genus and the equivariant super-slice genus. Using these bounds we
Externí odkaz:
http://arxiv.org/abs/2404.17062
Autor:
Cha, Jae Choon, Kim, Taehee
We show that for a winding number zero satellite operator $P$ on the knot concordance group, if the axis of $P$ has nontrivial self-pairing under the Blanchfield form of the pattern, then the image of the iteration $P^n$ generates an infinite rank su
Externí odkaz:
http://arxiv.org/abs/2402.04629
Autor:
Di Prisa, Alessio, Framba, Giovanni
Using Milnor invariants, we prove that the concordance group $\mathcal{C}(2)$ of $2$-string links is not solvable. As a consequence we prove that the equivariant concordance group of strongly invertible knots is also not solvable, and we answer a con
Externí odkaz:
http://arxiv.org/abs/2312.02058
Autor:
Ray, Arunima
Publikováno v:
Winter Braids Lect. Notes 8,Winter Braids XI (Dijon, 2021) (2021), Course 2, 31 pp
These notes were prepared to accompany a sequence of three lectures at the conference Winterbraids XI in Dijon, held in December 2021. In them, we provide an introduction to slice knots and the equivalence relation of concordance. We explain some con
Externí odkaz:
http://arxiv.org/abs/2311.12168
Autor:
Davis, Christopher William
In a groundbreaking work A. Levine proved the surprising result that there exist knots in homology spheres which are not smoothly concordant to any knot in $S^3$, even if one allows for concordances in homology cobordisms. Since then subsequent works
Externí odkaz:
http://arxiv.org/abs/2303.14509
In this brief note, we investigate the $\mathbb{CP}^2$-genus of knots, i.e. the least genus of a smooth, compact, orientable surface in $\mathbb{CP}^2\setminus \mathring{B^4}$ bounded by a knot in $S^3$. We show that this quantity is unbounded, unlik
Externí odkaz:
http://arxiv.org/abs/2210.12486
Autor:
Conway, Anthony
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 4575-4587
In the topological category, the classification of homotopy ribbon discs is known when the fundamental group $G$ of the exterior is $\mathbb{Z}$ and the Baumslag-Solitar group $BS(1,2)$. We prove that if a group $G$ is geometrically $2$-dimensional a
Externí odkaz:
http://arxiv.org/abs/2201.04465
We introduce a geometric operation, which we call the relative Whitney trick, that removes a single double point between properly immersed surfaces in a $4$-manifold with boundary. Using the relative Whitney trick we prove that every link in a homolo
Externí odkaz:
http://arxiv.org/abs/2104.06449