Zobrazeno 1 - 10
of 295
pro vyhledávání: '"Miller, Maggie"'
We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link be
Externí odkaz:
http://arxiv.org/abs/2406.11718
We study locally flat disks in $(\mathbb{C} P^2)^\circ:=(\mathbb{C} P^2)\setminus \mathring{B^4}$ with boundary a fixed knot $K$ and whose complement has fundamental group $\mathbb{Z}$. We show that up to topological isotopy rel. boundary, such disks
Externí odkaz:
http://arxiv.org/abs/2403.10080
We prove that the double branched cover of a twist-roll spun knot in $S^4$ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun knot connected sum with a trivial projective plane is preserved after
Externí odkaz:
http://arxiv.org/abs/2402.11706
We show that there exist split, orientable, 2-component surface-links in $S^4$ with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m,n$ with $m\ge 4$, the unlink $L_{m,n}$ consisting of one component of
Externí odkaz:
http://arxiv.org/abs/2307.12140
Autor:
Miller, Maggie
We give an explicit description of a fibration of the complement of the closure of a homogeneous braid, understanding how each fiber intersects every cross-section of $S^3$.
Comment: 19 pages, 18 figures. Written for the proceedings of "Frontier
Comment: 19 pages, 18 figures. Written for the proceedings of "Frontier
Externí odkaz:
http://arxiv.org/abs/2306.13081
We discuss an obstruction to a knot being smoothly slice that comes from minimum-genus bounds on smoothly embedded surfaces in definite 4-manifolds. As an example, we provide an alternate proof of the fact that the (2,1)-cable of the figure eight kno
Externí odkaz:
http://arxiv.org/abs/2303.10587
Autor:
Klug, Michael, Miller, Maggie
Let $S_0$ and $S_1$ be two homotopic, oriented 2-spheres embedded in an orientable 4-manifold $X$. After discussing several operations for modifying an immersion of a 3-manifold into a 5-manifold, we discuss the Freedman--Quinn (fq) and Stong (stong)
Externí odkaz:
http://arxiv.org/abs/2211.07177
We adapt Seifert's algorithm for classical knots and links to the setting of tri-plane diagrams for bridge trisected surfaces in the 4-sphere. Our approach allows for the construction of a Seifert solid that is described by a Heegaard diagram. The Se
Externí odkaz:
http://arxiv.org/abs/2210.09669
We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in $S^3$ that do not become isotopic when their interiors are pushed into $B^4$. In particular, we identify examples where the surfaces are not ev
Externí odkaz:
http://arxiv.org/abs/2205.15283