Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Cahn, Patricia"'
We give diagrammatic algorithms for computing the group trisection, homology groups, and intersection form of a closed, orientable, smooth 4-manifold, presented as a branched cover of a bridge-trisected surface in $\mathbb{S}^{4}$. The algorithm take
Externí odkaz:
http://arxiv.org/abs/2308.11689
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
A Fox p-colored knot $K$ in $S^3$ gives rise to a $p$-fold branched cover $M$ of $S^3$ along $K$. The pre-image of the knot $K$ under the covering map is a $\dfrac{p+1}{2}$-component link $L$ in $M$, and the set of pairwise linking numbers of the com
Externí odkaz:
http://arxiv.org/abs/2112.14790
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
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
Autor:
Cahn, Patricia, Kjuchukova, Alexandra
Kjuchukova's $\Xi_p$ invariant gives a ribbon obstruction for Fox $p$-colored knots. The invariant is derived from dihedral branched covers of 4-manifolds, and is needed to calculate the signatures of these covers, when singularities on the branching
Externí odkaz:
http://arxiv.org/abs/1812.09553
Autor:
Cahn, Patricia, Kjuchukova, Alexandra
Consider a dihedral cover $f: Y\to X$ with $X$ and $Y$ four-manifolds and $f$ branched along an oriented surface embedded in $X$ with isolated cone singularities. We prove that only a slice knot can arise as the unique singularity on an irregular dih
Externí odkaz:
http://arxiv.org/abs/1710.11562
Autor:
Cahn, Patricia, Kjuchukova, Alexandra
Let $M$ be a connected, closed, oriented three-manifold and $K$, $L$ two rationally null-homologous oriented simple closed curves in $M$. We give an explicit algorithm for computing the linking number between $K$ and $L$ in terms of a presentation of
Externí odkaz:
http://arxiv.org/abs/1611.10330
We study mapping class group orbits of homotopy and isotopy classes of curves with self-intersections. We exhibit the asymptotics of the number of such orbits of curves with a bounded number of self-intersections, as the complexity of the surface ten
Externí odkaz:
http://arxiv.org/abs/1603.00846
Publikováno v:
Algebr. Geom. Topol. 18 (2018) 1323-1360
In a 1983 paper with Frank Warner, we proved that the space of all great circle fibrations of the 3-sphere S^3 deformation retracts to the subspace of Hopf fibrations, and so has the homotopy type of a pair of disjoint two-spheres. Since that time, n
Externí odkaz:
http://arxiv.org/abs/1502.03428