Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Kjuchukova, Alexandra"'
Autor:
Cahn, Patricia, Kjuchukova, Alexandra
Let $K\subset S^3$ be a knot and $\eta, \gamma \subset S^3\backslash K$ be simple closed curves. Denote by $\Sigma_q(K)$ the $q$-fold cyclic branched cover of $K$. We give an explicit formula for computing the linking numbers between lifts of $\eta$
Externí odkaz:
http://arxiv.org/abs/2308.05856
We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Cappell and Shaneson's Meridional Rank Conjecture for these knots. In addi
Externí odkaz:
http://arxiv.org/abs/2208.09032
We study the $\mathbb{CP}^2$-slicing number of knots, i.e. the smallest $m\geq 0$ such that a knot $K\subseteq S^3$ bounds a properly embedded, null-homologous disk in a punctured connected sum $(\#^m\mathbb{CP}^2)^{\times}$. We give a lower bound on
Externí odkaz:
http://arxiv.org/abs/2112.14596
Autor:
Hayden, Kyle, Kjuchukova, Alexandra, Krishna, Siddhi, Miller, Maggie, Powell, Mark, Sunukjian, Nathan
This paper investigates the exotic phenomena exhibited by links of disconnected surfaces with boundary that are properly embedded in the 4-ball. Our main results provide two different constructions of exotic pairs of surface links that are Brunnian,
Externí odkaz:
http://arxiv.org/abs/2106.13776
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 75-85
We prove the meridional rank conjecture for arborescent links associated to plane trees with the following property: all branching points carry a straight branch to at least three leaves. The proof involves an upper bound on the bridge number in term
Externí odkaz:
http://arxiv.org/abs/2008.00763
Publikováno v:
Ann. Inst. Fourier (Grenoble) 74 (2024), no. 2, 849-866
We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^4$, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admit
Externí odkaz:
http://arxiv.org/abs/1909.11788
We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on meridional ra
Externí odkaz:
http://arxiv.org/abs/1907.02982
We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.
Comment: 6 pages, 3 figures, 0 footnotes. To appear in Proceedings of t
Comment: 6 pages, 3 figures, 0 footnotes. To appear in Proceedings of t
Externí odkaz:
http://arxiv.org/abs/1902.05721
Let $X^4$ and $Y^4$ be smooth manifolds and $f: X\to Y$ a branched cover with branching set $B$. Classically, if $B$ is smoothly embedded in $Y$, the signature $\sigma(X)$ can be computed from data about $Y$, $B$ and the local degrees of $f$. When $f
Externí odkaz:
http://arxiv.org/abs/1901.05858
Autor:
Cahn, Patricia, Kjuchukova, Alexandra
Publikováno v:
Algebr. Geom. Topol. 20 (2020) 1939-1963
Let $K\subset S^3$ be a Fox $p$-colored knot and assume $K$ bounds a locally flat surface $S\subset B^4$ over which the given $p$-coloring extends. This coloring of $S$ induces a dihedral branched cover $X\to S^4$. Its branching set is a closed surfa
Externí odkaz:
http://arxiv.org/abs/1812.10842